Download test two

c2 = a2 + b2 − 2ab cos C
name:
s
A
1 + cos A
cos = ±
2
2
Mathematics 142 second test
Wednesday, May 13, 2009
please show your work to get full credit
s
A
1 − cos A
sin = ±
2
2
1–2. Find the exact value of each expression by using an angle addition or subtraction
formula.
1.
sin 65◦ cos 70◦ + cos 65◦ sin 70◦
2.
cos 230◦ cos 80◦ + sin 230◦ sin 80◦
3–4. Find all the solutions between 0 and 2π for each trigonometric equation:
√ 3.
cot θ + 3 (csc θ − 2) = 0
4. cos 2θ + 4 sin2 θ = 0
page two
√
5. Convert (x, y) = (4, −4 3) to polar coordinates (r, θ).
6. Convert the polar equation r = 4 cos θ to
an equation involving x and y.
(HINT: First multiply both sides of the equation by r.)
7–8. Solve for the indicated side length or angle measure:
4
90°
20
x
A
5
25°
10
A
page three
9. Show that 5 cos2 θ + 2 sin2 θ = 5 − 3 sin2 θ.
10. Use the data
sin A =
2
and A is in quadrant two
3
cos B =
1
and A is in quadrant one
4
to compute exact values of
(a) cos A and sin B
(b) cos(A + B)
(c) sin 2A
(d) cos
B
2
page four
11. Use the graph of polar coordinate r versus direction angle θ ( in degrees ) to draw the
corresponding polar graph:
3 r 2 1 0 ‐210 ‐180 ‐150 ‐120 ‐90 ‐60 ‐30 ‐1 ‐2 ‐3 waterproof – paper.com
0 30 60 θ
90 120 150 180 210 page four
12. Show that cos tan−1 v = √
1
1 + v2
13. Show that cos(5θ − θ) − cos(5θ + θ) = 2 sin 5θ sin θ