STUDY, STUDY, STUDY!

Unit 4 Multiple Choice test (retake) tomorrow! 15-20 minutes when the bell rings!

Tonight, study! Look over the 10 pre-test questions that I gave you in class last week (or below). Remember, tomorrow's test is the same questions with different numbers! Study, study, study!

• You will have 15-20 minutes to complete the 10 multiple choice. Study so you know what you're doing! 
• This will count as a (4th) test grade for this quarter for everyone, regardless of the first test score! Get an A+!
• Prepare yourself to do well and take advantage of this opportunity!

Lastly, here are the answers to the "pre-test" so you can check your work, along with some explanations!

1. B (Remember, complements have to sum/add to 90 degrees, or pi/2 radians...so we need to subtract the angle measure given from pi/2--which requires a common denominator. OR, since you have a calculator, convert everything to degrees to find the answer (remember, pi = 180 degrees). So, this angle = 180/10, or 18 degrees; so the supplement must be 72 degrees! We can then convert each answer to degrees to see which one matches!)
2. D (For this question, mark each of the axes with the angle measures. For instance, we know pi/2 will be 7.5pi/15. We know pi = 15pi/15, and we know 2pi = 30pi/15. We can then use these as references to figure out which quadrant the terminal side falls in.) (OR, maybe it helps to convert the angle to degrees--plug in 180 for pi! So we can do -31x180/5 to find this angle in degrees, then determine the quadrant!)
3. B (Unit circle! This question is simply asking for the coordinate pair for this angle. Draw the angle, then use special triangles to find the x/y coordinates.) (OR, think about this...let's focus on the x coordinate...we know the x coordinate is cosine. So let's type cos(-240) in our calculator--make sure it's degree mode!. If we enter cos(-240) we get -1/2, so we know the xcoordinate has to be -1/2! So the answer must be B!)
4. B (This is a weird question...I would start  by looking at which sides (a,b,c) are used, and which angle they focus on. In this question, we're focusing on the 45 degrees (our theta), and we're using sides a (opposite) and b (adjacent). If we're using opposite and adjacent, this must be tangent!)
5. B (Remember these word problems? You were good at them! To start, draw a triangle; label the angle measure and side length given. Also label the side you're looking for with a variable. Now, decide which trig ratio you have to use--in this question, we're given the hypotenuse (ladder), and trying to find the opposite side--so we'll have to use sine. We know sin(62)=x/20! Set up the equation, cross multiply, and solve!) (Also, think about this...we know the hypotenuse, the longest side, is 20, so the answer must be less than 20--so we can at least narrow it down to two answers!)
6. B (This is straight from our most recent notes! Either use A/S/T/C (All student take calc) OR think about the x and y coordinates to determine where each inequality is true! Remember, >0 means positive, and <0 means negative.)
7. B (Again, straight from our most recent notes. For this question, first determine which quadrant the angle falls in (like #6). Then, draw a triangle in this quadrant, labeling your reference angle as theta.) (OR, think about this...they give us tangent, so that's the "opposite over adjacent." So we know the adjacent side is 5...this question asks us for cosine, which is "adjacent over hypotenuse," so we know the numerator = adjacent = 5. The answer must be B or D. Then, since tangent is negative and sine is negative, we must be in quadrant 4--in quadrant 4, cosine is positive, so the answer is B!)
8. D (More from our most recent notes! Plot the point; then, draw a triangle to the x axis. Label two sides of the triangle using the coordinates. Then, label your reference angle as theta. Now, use SOHCAHTOA to find the indicated ratio!)
9. A (Start by labeling each axis with the appropriate angle measures, but in radians "as decimals." For example, we know pi = 3.14 and 2pi = 6.28. For this question, remember we're looking at a negative angle, so -pi/2 = -1.57 (the bottom of the y-axis). The top of the y axis, or -3pi/2 = -4.71. We can then use these four points as a guide--which two values does our angle fall between? This will help us find which quadrant the angle falls in. For this question, -3.4 falls between -3.14 and -4.71, so this must be in quadrant 2. Then, for the reference angle, we'll take 3.4 - 3.14!)
10. D (Back to the unit circle! First, sketch the angle in standard position. Then, use your unit circle to find the coordinates OR draw a triangle formed with the x-axis, and label the sides using special triangles. Then, we have to think about our ratio--in this case, cotangent = x/y, so we take our x value divided by our y-value!) (Here's another way: make sure your calculator is in degree mode, and then enter 1/tan(-390). Write down this decimal. Then, convert each multiple choice option to a decimal to see which one matches!)