Download Alternate Final Exam Review

MATH 1330
Final Exam Review
1. Evaluate the following
expression:
sin
37𝜋
6
𝑐𝑜𝑠
𝑡𝑎𝑛 5𝜋
31𝜋
−
3
2. Let P(x,y) denote the point where the terminal
side of an angle 𝜃 meets the unit circle. If P is in
2
Quadrant IV and 𝑥 = find sin 𝜃 and tan 𝜃.
7
3. Given the following:
𝜋
0 < 𝑥 < , 0 < 𝑦 < 𝜋 , sin 𝑥 =
cos 𝑦 =
Evaluate:
cos(𝑥 − 𝑦)
5
8
2
2
5
,
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:
−1 −4
tan sin
5
9. Given ∆𝐴𝐵𝐶 with ∠𝐴 = 120 , ∠𝐵 = 30 , and
BC = 8 cm. Find AC. (All answers are in cm.)
2𝑥
10. Let 𝑓 𝑥 = ln 𝑥 and 𝑔 𝑥 = 𝑒 . 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
2
given parabola. 𝑦 − 2𝑥 + 2𝑦 − 13 = 0
13. Solve the following equation over the interval
2𝜋
[0, ]: 4 sin 5𝑥 + 2 = 4
5
14. Evaluate the following expression:
−1 1
sin
+ cos −1 −1 + tan−1 (− 3 )
2
15. Find the magnitude: v = 2 i  5 j
18. State the coordinates of the vertices for the
𝑥2
𝑦2
given ellipse.
+
=1
36
49
19. Write the equation
2
2
2𝑥 + 2 𝑦 − 6 = 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
𝜋
horizontal shift is units to the left, the vertical
3
𝜋
shift is 3 units up and the period .
9
24. Solve the following equation on the interval
[0, 2𝜋).
4𝑠𝑖𝑛2 𝑥 − 3 = 0
25. Triangle ABC has sides measuring 3 in, 7in, and
9 in. Determine the value of cos A, where A is the
largest angle.