WinsDay Homework

Tonight, please complete the "Trig Functions and the Unit Circle: Quiz" worksheet that we started in class!

Tomorrow we'll get back to the unit circle and keep practicing!

Don't forget, QUIZ FRIDAY--I give you a blank unit circle, you fill it out!

See you tomorrow!

2sDay HW

Tonight, please complete the following in your textbook: 

page 264: 21, 29, 31, 33, 35

Don't have your book? Here are the problems! :)

21.) Find sine, cosine, and tangent: theta = -3pi/2

Evaluate each:

29.) sin(5pi)

31.) cos(8pi/3)

33.) cos(-13pi/6)

35.) sin(-9pi/4)

Monday HW!

Back to work with this unit circle thing tomorrow!

Tonight, please complete the (blank) unit circle provided in class! 

• Label all angle measures in radians!
• Label all angle measures in degrees!
• Label the coordinates for each point on the unit circle!

**I know you can easily look these answers up online, or in the textbook. However, we will have a quiz (in a couple days) where you are given the same unit circle, and you have to fill it out on your own! If you do this independently tonight, you'll be ready for the quiz! If you simply look up the answers, you won't be prepared for the quiz!

Weekend HW: Investigate!

This weekend, please complete the "Sine, Cosine, and Tangent Investigation" provided in class.

• Just as you developed the unit circle on your own, this homework pushes you to "figure out" some of the new stuff we'll discuss next week!
• The more time/effort you put into (successfully) completing this and understanding it, the easier your upcoming week will be!
• Check below for some help if you get stuck!
• Questions 3-8 are dependent upon you finishing #2--if you're stumped, use my copy of the homework  below (with notes/hints) to help!

Good luck! This investigation will DEFINITELY be checked (as homework) on Monday! We'll jump right into our new notes--we'll review how to make that unit circle, and then start to evaluate trig functions on the unit circle!

Enjoy your weekend! Hope you aced our test today!

Homework (Investigation) Hints:

• **You may have to save the picture (if you're using a computer) to zoom in more

Homework Questions (Blank Worksheet):

TEST TOMORROW!

Study, study, study, study, study, study, study, study, study, study, study, study. And study outside! :)

If you'd like to do some practice problems to study, check these out--all of this stuff is on your test! (And the answers are in the back of your book). Feel free to stop by tomorrow morning before 7:30 (or C period) if you have any quick questions.

Page 333: 3, 5, 7, 9, 11, 13, 15, 17, 27, 31, 57, 59, 63, 65, 67, 79, 81, 91, 93

I would also recommend looking at your past quizzes to study!

Here's a list of what's on your test: (textbook section # in parentheses)

• Use a graphing calculator to evaluate trig functions (4.3)
• Ex: sin(2.34) = ?, cos(154 degrees) = ?, sec(2pi/3) = ?, cot(139 degrees) = ?
• SOHCAHTOA "Word Problems" (4.3)
• Draw a triangle to model the scenario
• Use trig ratios to find a missing side length
• Use trig inverses to find missing angle measures
• Know angles of elevation and angles of depression (how to draw them)
• Solve triangles (4.3)
• Use trig ratios and/or trig inverses to find all side lengths and angle measures
• Also, use Pythagorean theorem! And know that angles of a triangle sum (add up to) 180 degrees!
• Define the 6 trig ratios given a triangle (and "theta") (4.3)
• Be sure you know the 6 ratios! Study, study, study!
• Define the (remaining 5) trig ratios given one ratio (4.3)
• Example: Given sin(x) = 3/5, draw a triangle, choose/identify an angle theta, find the third side of the triangle (Pythag.), and then define the remaining 5 ratios!
• Convert angle measures to radians (4.1)
• Convert angle measures to degrees (4.1)
• Find complements and supplements in degrees (4.1)
• Find coterminal angles (+/-) in degrees (4.1)
• Find complements and supplements in radians (4.1)
• Use common denominators/fractions to solve--no converting to degrees!
• Find coterminal angles (+/-) in radians (4.1)
• Sketch angles in standard position (radians and degrees) (4.1)
• Find the measure of a reference angle
• Remember, reference angles are formed by the terminal side of an angle and the X axis!

Unit Circle! And test Friday!

GREAT work today! You all did an awesome job working together to figure out something tough, the unit circle! Tomorrow we'll recap our work and continue to develop our understanding of the unit circle, and start to connect it to the rest of our trig stuff!

Tonight, your homework is to finish your unit circle (classwork) if you didn't already. The completed product must have each of the following:

• Each angle measure labeled in degrees
• Each angle measure labeled in radians
• All coordinate pairs labeled for each angle 

If you get stuck, here are the "hint cards" for each question:

• 2.) Consider the radius of the circle. Remember, each of these points on the axes (x or y axis) is a radius; we can use this information to figure out “how far right/left” or “how far up/down” we have moved, and then this will help us label the coordinates.
• 4.) This is a 45° angle, so we must have to use special triangles somehow.
  Draw yourself the “reference triangle.”Now can you label the sides of the triangle (based on the properties of a 45/45/90 triangle)? Use these side lengths to determine the x (“how far right”) and y (“how far up”) coordinates.
• 5.)Think the same way you did for #4. Draw that reference triangle, then use the properties of a 30/60/90 triangle to label the side lengths and determine the x and y coordinates (how far right, how far up?)
• 6.) See 4 and 5. You got this.
• 7.) Think about the activity where we shaded our angle measures on blank circles. For this, we split up our circles by π/4’s or π/3’s or π/6’s. You likely have these pictures in your notes (you better! :) ) Also, consider using “X” shapes…extend the lines you drew in the first quadrant into the 3^rd quadrant. 
• 8.) There are two ways to think about finding the coordinates where the angles intersect the unit circle for the remaining 3 quadrants…
  Method 1: Think about reflections…consider how the sign (+/-) of the x and y values differ for each quadrant. Then, consider the reference angle. Use the coordinates from quadrant 1 for the same reference angle, and then simply use reflections to change the signs (+/-) appropriately.
• 8.) Method 2: For any angle measure, draw the reference triangle—remember, we always draw our triangles to the x-axis (remember the bowtie?). When we do this, we will create a special triangle (30/60/90 or 45/45/90). We can now use the properties of special triangles to label the side lengths, and thus find the x and y coordinates. Just remember to pay attention to the signs (+/-).

Also, don't forget....TEST FRIDAY! (There is no unit circle stuff on our test).

Here's a list of what's on your test: (textbook section # in parentheses)

• Use a graphing calculator to evaluate trig functions (4.3)
• Ex: sin(2.34) = ?, cos(154 degrees) = ?, sec(2pi/3) = ?, cot(139 degrees) = ?
• SOHCAHTOA "Word Problems" (4.3)
• Draw a triangle to model the scenario
• Use trig ratios to find a missing side length
• Use trig inverses to find missing angle measures
• Know angles of elevation and angles of depression (how to draw them)
• Solve triangles (4.3)
• Use trig ratios and/or trig inverses to find all side lengths and angle measures
• Also, use Pythagorean theorem! And know that angles of a triangle sum (add up to) 180 degrees!
• Define the 6 trig ratios given a triangle (and "theta") (4.3)
• Be sure you know the 6 ratios! Study, study, study!
• Define the (remaining 5) trig ratios given one ratio (4.3)
• Example: Given sin(x) = 3/5, draw a triangle, choose/identify an angle theta, find the third side of the triangle (Pythag.), and then define the remaining 5 ratios!
• Convert angle measures to radians (4.1)
• Convert angle measures to degrees (4.1)
• Find complements and supplements in degrees (4.1)
• Find coterminal angles (+/-) in degrees (4.1)
• Find complements and supplements in radians (4.1)
• Use common denominators/fractions to solve--no converting to degrees!
• Find coterminal angles (+/-) in radians (4.1)
• Sketch angles in standard position (radians and degrees) (4.1)
• Find the measure of a reference angle
• Remember, reference angles are formed by the terminal side of an angle and the X axis!

Tuesday = Start Studying!

No formal homework tonight!

I added a link to a "textbook companion site" that goes along with your textbook! I also added Ms. Blaisdell's class page! Check them out!

Tomorrow we will continue with our "new stuff," developing the unit circle! This unit circle will serve as the foundation for the majority of our work for the next couple months!

Of course we have our first test on Friday! Start studying now! I will be after school tomorrow if you need help, but Thursday is a half day so I won't be here!

Here's a list of what's on your test: (textbook section # in parentheses)

• Use a graphing calculator to evaluate trig functions (4.3)
• Ex: sin(2.34) = ?, cos(154 degrees) = ?, sec(2pi/3) = ?, cot(139 degrees) = ?
• SOHCAHTOA "Word Problems" (4.3)
• Draw a triangle to model the scenario
• Use trig ratios to find a missing side length
• Use trig inverses to find missing angle measures
• Know angles of elevation and angles of depression (how to draw them)
• Solve triangles (4.3)
• Use trig ratios and/or trig inverses to find all side lengths and angle measures
• Also, use Pythagorean theorem! And know that angles of a triangle sum (add up to) 180 degrees!
• Define the 6 trig ratios given a triangle (and "theta") (4.3)
• Be sure you know the 6 ratios! Study, study, study!
• Define the (remaining 5) trig ratios given one ratio (4.3)
• Example: Given sin(x) = 3/5, draw a triangle, choose/identify an angle theta, find the third side of the triangle (Pythag.), and then define the remaining 5 ratios!
• Convert angle measures to radians (4.1)
• Convert angle measures to degrees (4.1)
• Find complements and supplements in degrees (4.1)
• Find coterminal angles (+/-) in degrees (4.1)
• Find complements and supplements in radians (4.1)
• Use common denominators/fractions to solve--no converting to degrees!
• Find coterminal angles (+/-) in radians (4.1)
• Sketch angles in standard position (radians and degrees) (4.1)
• Find the measure of a reference angle
• Remember, reference angles are formed by the terminal side of an angle and the X axis!

Monday HW

Tonight, please complete the 4 word problems provided in class (or below)!

Great work today everyone! I loved seeing you all working hard and helping each other out! Keep it up!

Tomorrow we'll start a new section, 4.2--and start learning about the unit circle!

And don't forget--test Friday! 

Here's your homework in case you lost it (or were out)!

Directions: Each question is worth 3 points: 1 point for drawing the correct picture, 1 point for setting up an equation using the proper trigonometric function, and 2 points for finding the correct answer (with units!!!!). In your picture you should label the given sides/angles, and unknown sides/angles. Good Luck!

1. A boy flying a kite lets out 300 feet of string which makes an angle of 38 with the ground. Assuming that the string is straight, how high above the ground is the kite?

2. A straight road to the top of a hill is 2500 feet long and has a 12 angle of elevation. Find the height of the hill.

3. A 25-foot ladder leans against a building. The ladder’s base is 13.5 feet from the building. Find the angle which the ladder makes with the ground.

4. During one of your many snow days, you built a ramp to sled off of. The ramp is 10 feet long and 3 feet high. What is the angle of elevation of the ramp? 

Weekend Homework

This weekend:

1.) Complete the "word problems" we started and drew pictures for in class today. THIS WILL BE COLLECTED AND GRADED ON MONDAY! (Use the pictures below!)

2.) Solve the two triangles provided in class or below. 

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Here's a copy of the worksheet that I'm collecting on Monday in case you lost yours (the diagrams above are for these questions):

Trigonometry: Solving Right Triangles

1.) A person is looking up at a hot air balloon; the angle of elevation to the balloon is 45.° The distance from the observer to the basket of the balloon is 100 feet. How high is the balloon?

2.) A ladder leans against a house at an acute angle, while the house and ground form a right angle. The ladder is 17 feet long, its base sits 8 feet away from the house.

a. Find the six trigonometric ratios for the acute angle formed by the ladder and ground.

b. Find the measure of the acute angle formed by the ladder and the ground.

3.) Claire is standing on top of a 30 ft. lookout tower on shore keeping an eye on a cruise ship that is in the harbor docked.  If she is looking at the ship at an angle of depression of 12⁰ when the ship stops, how far do the passengers of the ship have to ride the fairy to the dock?

4.) When a 757-Passenger jet begins its descent on Bradley Airport, it is 4300ft from the ground.  Its angle of descent (depression) is 9^o.  Make a sketch.

a.      What is the plane’s ground (horizontal) distance to the airport?

b.      How far does the plane have to travel to reach the airport?

5.) Find the measure of the angle a in the diagram below.

6.) A diver stands on level ground 50 feet from the base of the 12 foot high dive. What is the approximate measure of the angle of elevation between the diver and the diving board (round to the nearest degree)?

7.) A kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. The angle of elevation formed by the string and the ground is 40°. Find the length of the string to the nearest foot.

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Lastly, we have a test coming up next week! Here's an outline of EVERYTHING we've covered so far that you'll need to know for your test!

• Section 4.1:
• Sketch angle measures in radians and degrees (in standard position)
• Name an angle measure in radians/degrees given a sketch
• Determine which quadrant the terminal side of an angle falls in
• Find complements and supplements in both radians and degrees
• Find coterminal angles in radians and degrees
• Convert angle measures from radians to degrees
• Convert angle measures from degrees to radians
• Section 4.3
• Define the 6 trig ratios for a triangle and given angle (theta)
• Sketch a triangle, label sides, and define the trig ratios given one ratio
• Ex: Given cos(x) = 1/3, find the remaining 5 trig ratios
• Solve triangles
• Use ratios to find side lengths
• Use trig inverses to find angle measures
• "Word Problems"
• Sketch a (right) triangle to model a scenario
• Know: angles of elevation, angles of depression
• Use SOHCAHTOA to find missing side lengths and/or angle measures

Thursday HW

Tonight, please complete the "More 4.3 Practice" worksheet provided in class. Check out these hints below...

• You need a calculator to complete this!
• For 1-4 we are asked to find angle measures--remember, that means we need to use the trig inverses on our calculator!
• For #2 (a and b), your challenge is to find all of the angle measures and side lengths...
• For a, I would use the Pythagorean Theorem to find the third side of the triangle; then, set up trig ratios and use trig inverses to find the remaining angle measures
• For b, you can find the third angle measure because you know the three angles must sum (add up to) 180 degrees; then, use 27.5 as your "theta" and try to set up trig ratios to find the missing two sides
• #3 is like two problems combined in one...try this...
• To find the height of the taller building, first focus on the "little" triangle with the 20 degree angle in it
• Set up a trig ratio to find the "opposite" side of this little triangle; and remember, you know the "adjacent" side is 60 ft.
• Then, focus on the "upside down triangle" with the 35 degree angle
• Again, set up a trig ratio to find the "opposite" side of this triangle; again, the "adjacent" side is 60 ft.
• What do we have to do with these two answers to find the total height of the taller building?
• For #4, set up a trig ratio and then use trig inverses to find the angle measure between the ladder and the ground (theta).
• Based on this answer, is the ladder safe? (Safe means our angle can be no greater than 75 degrees...)
• For #5, remember that when you draw your triangle, the angle of depression is "outside" your triangle (at the top). Use this information to find the angle at the top on the "inside" of the triangle (these two angles must add to 90).
• Then, set up a trig ratio to find the "opposite" side given the "adjacent" side (125 ft.)
• For #6, draw a triangle...
• You should be trying to find the "opposite" side (height of the building) given the "adjacent" side (65 m. from the base).
• For #7, remember that "due North" refers to the vertical side and "east" refers to the horizontal side...
• Label your triangle with the given info--you know the "opposite" and "adjacent" sides of the triangle (for the theta given)
• Set up a trig ratio and use trig inverses to solve.

Good luck :)

Tomorrow we'll look at our homework and answer any questions; then, we'll get to some group work/practice!

On Monday we'll wrap up this section, and then we'll have our first test (likely next Wednesday)! Woohoo!

Quiz Tomorrow!

Study for your quiz! I'd recommend using these problems to study....(below). Your quiz is also 2 questions--just like these, but different numbers.

• Complete the two problems on the 4th slide of the powerpoint provided in class. (or below).
• Given cos(ϴ) = 3/7, find the values of the remaining 5 trigonometric functions.
• Define the 6 trig ratios for the angle θ in the triangle below:

2sDay HW!

Tonight, please complete the following in your textbook:

Page 274: 9, 13, 15

Enjoy! Tomorrow we'll get into the applications--every problem will require using sine, cosine, and tangent on a graphing/scientific calculator! Come to class prepared!

Have a great rest-of-Tuesday!

Monday HW!

Tonight, please complete the following in your textbook (based on today's notes!): 

Page 274: 1, 2, 3

(And I'm definitely checking homework tomorrow!)

Enjoy the rest of your Monday!

Weekend HW

This weekend, please complete the reference angles worksheet provided in class! 

Enjoy! Good luck! On Monday we'll go over these and start our next section! Enjoy! And have a great weekend!

Here's your plan for the next 17 Sundays...GO GMEN!

Quiz Tomorrow!

Tomorrow we will start class with a quiz on radian measure! Here's what's on it (same stuff as Tuesday's homework in the textbook):

• Find complements, supplements, and coterminal angles in radians (WITHOUT converting to degrees...because I'm going to give you "weird" radian measures)
• Convert angle measures from degrees to radians
• Determine which quadrant the terminal side of an angle falls in (angles given in radians)
• Sketch angle in standard position (in radians)
• Find complement and supplement of an angle in radians
• Name the measure of angles in radians (given a picture)

Enjoy! Tomorrow we'll wrap up this unit with some reference angles classwork, and then on Monday it's on to new stuff!

***Everything we're doing on Monday requires a graphing or scientific calculator. You HAVE to have one by Tuesday. (A scientific calculator is $10-$15).**

Tuesday HW

Tonight, please complete the following in your textbook:

Page 255: 5, 9, 11, 13, 15, 17, 19

Enjoy! Tomorrow we'll wrap up our first chapter with some classwork, and then we'll have a quiz on Thursday or Friday! Wooo!

Labor Day = Take Home Quiz!

This weekend, please complete your (radians) take home quiz provided in class! If you lost yours or you were absent, please email me and I'll forward you a copy! (carofano.fm@easthartford.org).

Take your time, do your best, get an A!

Have an awesome weekend! Rest up, relax, hang out with friends and family, and GO OUTSIDE! It's going to be beautiful!

As always, email (or use Remind) with any questions! See you all Tuesday for the last day of notes on section 4.1!

Thursday HW

No homework tonight!

Remember, tomorrow we have the STAR test in room 132! Be there!

This weekend you will have a take home quiz (which I will give you tomorrow)--be ready to get an A!

Enjoy your Thursday night and I'll see you manana! (I don't know how to do the tilde....or accent marks....)

Did you ace your quiz today?

I hope so!

Tonight, please complete the "Measuring Angles in Radians and Degrees" worksheet provided in class.

• Name each of the 15 angles in RADIANS AND DEGREES
• Remember, all of the answers are based on (or are multiples of) the special angles--30, 45, 60, 90 degrees.

Enjoy! See you all tomorrow for some more radians!

Quiz Tomorrow!

Tonight...study! 

Your quiz tomorrow will include the following--everything is in degrees:

• Sketch angle measures in standard position
• Determine which quadrant the terminal side of an angle falls in
• Name an angle measure in degrees (given a sketch)
• Find complements and supplements
• Find one positive, one negative coterminal angle
• Label the sides of the special triangles!

Good luck! Be ready to get an A!

Tomorrow in class we'll continue to investigate angle measures in radians...I can't wait! :) See you there!