Functions & Trigonometry Final Review #3. 3. Please find 2 coterminal angels (one positive and one negative) in the same measure as the given angle.

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1 1. Please convert the following angles to degrees. a. 5 3 revolutions CCW = b. 5π 9 = c. 9 12π 4 revolutions CW = d. 5 = 2. Please convert the following angles to radians. a. c. 3 5 revolutions CCW = b = 5 12 revolutions CW = d. 540 = 3. Please find 2 coterminal angels (one positive and one negative) in the same measure as the given angle. a. 500 b. 13π 4 c. 82,,, 4. Please identify the following: 24 C A Sin A = Sin B = Cos A = Cos B = Tan A = Tan B = 25 B Sec A = Sec B = Csc A = Csc B = Cot A = Cot B = 5. Please find m<b and m<a (from #4) to the nearest tenth of a degree. 6. Please find the length of an arc in a circle with diameter of 12 cm. and a central angle of a 7π 8. 1

2 7. Please find the length of an arc in a circle with a central angle of 107 and a radius of 3 inches. 8. When do you use the Law of Cosines? When do you use the Law of Sines? Use the following information for question 8 & 9. N M P 9. Please find the distance between M and P to the nearest tenth. 10. Please find m<p and m<m to the nearest tenth. Y X 24 Z 11. Please find the distance between X and Y and the distance between X and Z to the nearest tenth. 2

3 12. Given f x ( ) = 3cos 1 4 x + π 1 Please identify the following and sketch the graph: Amplitude: Period: Phase shift: Vertical shift: Domain: Range: 13. Given f x ( ) = 2sin( 2x + 8π ) + 5 Please identify the following and sketch the graph: Amplitude: Period: Phase shift: Vertical shift: Domain: Range: 14. Please find the image of the point (1, 0) after the given rotations. Please round your answers to 3 decimal places. a. R 154 : b. R 9π 7 : c. R 320 : d. R 4π 11 : 3

4 15. Please solve each of the following trig. equations for 0 θ 360 AND 0 θ 2π. Please round to 3 decimal places. a. sinθ =.893 b. cosθ =.278 c. tanθ = Please express the following in terms of sine and cosine. sec x = csc x = tan x = cot x = 17. Please find the following: a. cos π 4 b. sin π ( ) c. tan π 2 d. sec 5π 6 7π e. cot 4 f. csc 4π Which quadrants are each of the functions restricted to? sin -1 cos -1 tan -1 4

5 19. Please evaluate the following, without a calculator. a. sin -1 ( ) = b. cos -1 ( ) = c. cos -1 (0) = d. tan -1 ( ) = e. sin -1 ( ) = f. cos -1 (1) = g. tan -1 ( ) = h. tan -1 (-1) = 20. How many different triangles exist with the given characteristics? a. <A = 105 b. <A = 42 c. <A = 30 d. <A = 70 a = 10 a = 8 a = 17 a = 14 b = 12 b = 10 b = 15 b = Please find all solutions between 0 and 2. Then, give the general solution. a. 2cos x + 1 = 0 b. tan 2 x 3 = 0 c. 2sin x - 2 = 0 d. cos 2 x cos x - 2 = A desk drawer contains 3 red pens, 6 blue pens, and 8 pencils. If three writing utensils are pulled from the drawer in succession, what is the probability that the first is a red pen, the second is a blue pen, and the third is a pencil? 5

6 23. Five students race to get in line at the one open register at McDonalds. How many different lines (orderings) are possible? 24. How many different social security numbers are possible? 25. How many different outings are possible given a choice of 5 restaurants, 4 movies, and 2 houses to return to? 26. Three students are given a choice of cake, pie, or nothing for dessert. What is the probability that all 3 students choose pie? 27. What is the probability of an impossible event? What is the probability of a certain event? What is the sum of all the probabilities in the sample space? 28. There are 9 clear and 5 colored marbles in a bag. Three marbles are selected at random and replaced each time. What is the probability that a.) all three are clear? a. b.) none of the three are clear? b. c.) all three are clear if each marble is NOT replaced? c. 29. What is the Sample Space for a family with 3 children? 6