Test 1, MAT 137
Review 1, MAT 137
Change the following to their exact radian measure.
1.) 750
2.) 1000
3.) 2500
Change the following to their exact degree measure.
4.) [pic]
5.) 4 radians
6.) [pic]
7.) Find the arc length of a circular region with a central angle of [pic]and a radius of 7.5 m.
8.) Find the arc length of a circular sector with a central angle of 800 and a diameter of 12 cm.
9.) Find the area of the circular sector with a central angle of [pic]and a radius of 7.5 m.
10.) Find the complementary angle of[pic].
11.) Find the supplementary angle of[pic].
12.) Find the exact value of all the trigonometric functions on the angle of[pic].
13.) Find the exact value of all the trigonometric functions on the angle of[pic].
14.) Find the exact value of all the trigonometric functions on the angle of[pic].
15.) Find the exact value of all the trigonometric functions on the angle of[pic].
16.) Find the exact value of all the trigonometric functions on the angle of[pic].
17.) Find the exact value of all the trigonometric functions on the angle of[pic].
Suppose [pic] is a right triangle with [pic] and
18.) Given b = 12.0 and c = 19.5, find a.
19.) Given a = 17.43 and b = 11.97, find c.
20.) Given [pic] is acute and[pic], find
a.) [pic] b.) [pic]
c.) [pic] d.) [pic]
e.) [pic]
21.) Suppose[pic]is acute and[pic] What is [pic]
22.) A 30 foot ladder is leaned against a vertical wall and has a 72.50 angle of elevation with the level ground. To the nearest tenth of a foot, determine how high up the wall that the ladder reaches.
23.) When Jim is 40 feet from the base of a tree going up vertically, the angle of elevation to the top is 490. Determine the height of the tree.
24.) Let [pic] and [pic] Find the two solutions for [pic]
25.) Suppose[pic]. Find all the solutions for [pic]
26.) Suppose[pic]. Find all the solutions for [pic]
27.) Suppose[pic]find the exact value of the other 5 trigonometric functions.
28.) A guy wire is attached to the top of an antenna and to a point on level ground that is 25 feet from the base of the antenna. If the wire has an angle of elevation of 81.750 with the ground, approximate the height of the antenna to the nearest foot.
29.) Suppose [pic]
a. What is the amplitude?
b. What is the period?
c. What is the phase shift?
d. What is the vertical shift?
30.) Graph[pic] so that at least one full period is shown on the graph below. Show and label 5 key points [intercepts, maximums, minimums].
31.) Suppose [pic]
a. What is the amplitude?
b. What is the period?
c. What is the phase shift?
d. What is the vertical shift?
32.) Graph [pic]so that at least one full period is shown on the graph below. Show and label 5 key points [intercepts, maximums, minimums].
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