MATH 1330 Final Exam Review

1. Evaluate the following expression: sin 37𝜋 6 𝑐𝑜𝑠 − 31𝜋 3 𝑡𝑎𝑛 5𝜋

2. Let P(x,y) denote the point where the terminal side of an angle 𝜃 meets the unit circle. If P is in Quadrant IV and 𝑥= 2 7 find sin 𝜃 and tan 𝜃 .

3. Given the following: 0<𝑥< 𝜋 2 , 0<𝑦< 𝜋 , sin 𝑥 = 2 5 , cos 𝑦 = 5 8   Evaluate: cos(𝑥−𝑦)   

4. Evaluate: sin 330 − cos 120

5. Give all possible polar coordinates for the point −5 , −5 given in rectangular coordinates. (In the choices below, n represents any integer.)

6. Simplify: sin⁡(𝑥) 1−cos⁡(𝑥) + 1−cos⁡(𝑥) sin⁡(𝑥)

7. Given 𝑓 𝑥 =2 csc 5𝑥 . Find the vertical asymptotes for f(x).

8. Find the exact value of the expression: tan sin −1 −4 5

9. Given ∆𝐴𝐵𝐶 with ∠𝐴=120 , ∠𝐵=30 , and BC = 8 cm. Find AC 9. Given ∆𝐴𝐵𝐶 with ∠𝐴=120 , ∠𝐵=30 , and BC = 8 cm. Find AC. (All answers are in cm.)

10. Let 𝑓 𝑥 = ln 𝑥 and 𝑔 𝑥 = 𝑒 2𝑥 . Find 𝑓∘𝑔 7 .

11. A string running from the ground to the top of a fence has an angle of elevation of 60°. The fence is 6 feet tall. What is the length of the string?

12. State the coordinates of the focus for the given parabola

13. Solve the following equation over the interval [0, 2𝜋 5 ]: 4 sin 5𝑥 +2=4

14. Evaluate the following expression: sin −1 1 2 + cos −1 −1 + tan −1 (− 3 )

15. Find the magnitude: v = 2 i  5 j

18. State the coordinates of the vertices for the given ellipse

19. Write the equation 2𝑥 2 + 2 𝑦−6 2 =72 to polar coordinates.

20. Give tan 𝑥 =−3 and 0<𝑥<𝜋: find the value for sin 2𝑥 .

21. Given vectors: u = < 6,  8>, v = < 4, 5 > , find u·v.

22. Given vectors: u = < 2,  3>, v = < 7, 5 > , 3u – 2v

23. Find a sine function with positive vertical displacement satisfying : The amplitude is ½ , the horizontal shift is 𝜋 3 units to the left, the vertical shift is 3 units up and the period 𝜋 9 .

24. Solve the following equation on the interval [0, 2𝜋)

25. Triangle ABC has sides measuring 3 in, 7in, and 9 in 25. Triangle ABC has sides measuring 3 in, 7in, and 9 in. Determine the value of cos A, where A is the largest angle.