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 3rd 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!
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