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Mathematics 142 first test
Wednesday, April 22, 2009
please show your work to get full credit
1. Convert
3π
radians to degrees.
10
2. An central angle of 28◦ intercepts an arc of a circle of radius 400 centimeters.
(a) Find the radian measure of the angle.
(b) Find the length of the intercepted arc.
3. The terminal side of angle A in standard position intersects the unit circle at the point (x, y) =
−12 5
,
13
13
Write down the values of the six trigonometric functions of A.
4. The inverse trigonometric equation
cos−1 n = A
is equivalent to the
trigonometric equation
5. Find the exact value of cos
, with angle restriction
≤A≤
5π
(Your answer should involve square roots. Don’t give a decimal approximation)
6
page two
6. How many solutions does each of the following equations have? (It is not necessary to write down the
solutions)
(a) cos A =
3
4
(b) csc θ = 3
7. Find all the solutions of
√
sin θ = −
2
2
9. Use a calculator to estimate the value of
(a) cot
π
5
(b) sec−1 (−2)
(c) tan−1 x =
π
3
(d) sin−1 x = π
8. Find all the solutions between 0 and 2π of
π 1
=
cos θ −
4
4
3
10. Find the exact value of tan cos−1
10
page three
11. True or False ?
(a) cos(−A) = − cos A
(c) cot 90◦ is undefined
(b) tan(A + π) = − tan A
30
20
−
5π
, 0
12
10
0
19π
, 0
12
‐10
‐20
‐30
12. For the sinusoidal graph shown above
(a) State the amplitude:
(b) What is the period?
(c) Find an equation for the graph in the format y = A sin(ωx − C)
page four
13. Sketch a graph of
y = 80 cos (30x)
Be sure your graph includes the exact location of all quarter-cycle points.
14. Specify the locations of the vertical asymptotes to the graph of f (x) = tan
x
60