Download − +−= 4 π 2x csc 31 y

PLANE TRIGONOMETRY – MATH 1213 – Test 2 covers Ch 4.3-8.3 (+cumulative) Summer I, 2008 – Olson
READ DIRECTIONS CAREFULLY.
Name (First Last):
Total is out of 100 pts. EQUIPMENT: pencil, eraser, color pencils, ruler, calculator, departmental Trig
formula sheet. Show all work on the paper here. Step DOWN between steps. Circle the final answer on multistep (non-graph) problems. IF more space is needed to finish a problem, say “see back” and put just the finish
on the back of another page. (Graph paper and extra blank paper is also available upon request.) Little credit
will be given for unsupported answers. Each problem is 5 points each unless otherwise marked. (Projected time
needed is ≈ 75 minutes.) Good LuckJ, remember good test-taking strategies, and to breathe.
1) (10 pts) Given the function below
a) Find: the reciprocal function, the amplitude of the reciprocal function
b) The period, any phase shift, any vertical shift, any x-axis reflection of the given function.
c) Find 5 key points of the reciprocal function.
d) Manually graph the function over a two-period interval.
π

y = −1 + 3 csc  2x − 
4

2) An object is attached to a coiled spring. It is pulled
down a distance of 6 units from its equilibrium
position and then released. The time for one
complete oscillation is 4 sec.
a) Write an equation that models the position of
the object at time t.
b) Determine the position at t = 1.25 sec.
c) Find the frequency.
3) Given cos s =
5
and tan s < 0, find the
5
exact value for sin s.
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4) (10 pts) Verify that the trigonometric equation is an identity.
(sec α – tan α)2 =
1 − sin α
1 + sin α
5) (6 pts) Use identities to find the exact value of (a) cos (s – t), (b) sin (s + t), and (c) tan (s + t). (Do not use a
calculator.)
3
5
cos s = and sin t = , s and t in quadrant II
5
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6) (6 pts total) a) Write the expression in terms of
a single trigonometric function.
2 tan 4θ
1 − tan 2 4θ
b) Write the expression as a sum or difference of
trigonometric functions.
sin 4x sin 5x
7) Evaluate. (Do not use a calculator.)
cos
7π
π
− cos
12
12
8) Find the exact value of the given expression.
(Do not use a calculator.)

 5 
cos arcsin −  
 13  

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9) Solve the equation over the interval [0°, 360°).
cos 2θ – sin2θ = 1
12) (10 pts) Solve each triangle ABC that exists.
a) A = 61.7°, a = 78.9 m, b = 86.4 m
b) A = 51° 20΄, c = 68.3 m, b = 58.2m
10) Solve the equation for exact solutions over the
interval [0, 2π).
cos 2x + cos x = 0
13) A balloonist is directly above a straight road 1.5
mi long that joins two towns. She finds that the
town closer to her is at an angle of depression of
35°, and the farther town is at an angle of
depression of 31°. How high above the ground
is the balloon?
35°
31°
11) (3 pts) Find the area of the triangle ABC.
A = 30.50°, b = 13.00 cm, C = 112.60°
Town
Town
1.5 mi
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14) (4 pts) Find the magnitude and direction angle
for the vector.
18) Find the sum of the pair of complex numbers
geometrically.
5 – 6i, –2 + 3i
u = 〈15, –8〉
15) Determine whether the vectors 〈1, 2〉 and
〈–6, 3〉 are orthogonal.
16) A force of 30 lb is required to hold a 60-lb
stump grinder on an incline. What angle does
the incline make with the horizontal?
19) Find the quotient and write it in rectangular
form. First convert the numerator and
denominator to trigonometric form.
2i
−1− i 3
17) Find the product and write it in rectangular
form.
(6 cis 120°)[5 cis(–30°)]
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