Math 104 Final Review
1.Find all six trigonometric functions of if is on the terminal side of .
2.Find and if the terminal side of lies along the line in
quadrant IV.
3.Find the remaining trigonometric functions of if and terminates
in quadrant II.
4.Use identity substitutions to simplify: a) b)
5.Show that by transforming the left side into the right side.
6.Simplify the expression as much as possible after substituting for x.
7.If with in quadrant I, find , , and .
8.In which quadrant will lie if and ?
9.In , C = , c= 4.79 cm, and b = 3.68 cm. Draw the triangle then find each of the following: a) Side a b) Angle A c) Angle B
10.In C = , A = , and side a = 12 cm. Find exact answers for each of the
following.a) Side cb) Side b
11.Use a calculator to find: a) b) if is acute and
12.A CB antenna is located on the top of a garage that is 16 feet tall. From a point on level ground that is 100 feet from a point directly below the antenna, the antenna subtends an angle of . Approximate the length of the antenna.
13.A pilot, flying at an altitude of 5000 feet, wishes to approach a landing point on a runway at an angle of (angle of depression). Approximate, to the nearest 100 feet, the distance from the airplane to the landing point at the beginning of the descent.
14.Give the exact values of: a) b) c)
15.Find the exact values of: a) b) c) (Simplify)
16.Show that cotangent is an odd function.
17.Convert to radians: a) b)
18.Convert to degrees: a) b)
19.Draw the following angles in standard position and find the reference angle:
a) b) c)
20.Use a calculator to find if is between and and
a) with in quadrant III
b) with in quadrant IV
21.If is a central angle that subtends an arc length of , find the radius of the circle.
22.Find the area of the sector formed by central angle in a circle of radius
23.A conical paper cup is constructed by removing a sector from a circle of radius 5 inches and attaching edge OA to OB (see figure). Find angle AOB so that the cup has a depth of 4 inches.
24.Find the amplitude, period, and phase shift of:
a.
b.
25.Sketch one period of:
a.
b.
c.
d.
26.Find the equations of each of the following:
a.
b.
c.
27.Find an interval over which the graph of completes one complete cycle.
28.Find the range of .
29.Find the exact value for each of the following:
a.b.c.
30.Find the exact values for each of the following:
a.b.
31.Find the exact value for each of the following:
a.b.
c.d.
32.If , rewrite is terms of x without trig functions.
33.Let with in the second quadrant and with in the third quadrant. Compute .
34.a. Derive the formula for using the formulas for sine and cosine.
- Find if and .
35.If x is a positive number, find:
a.b.
36.Find the exact values of:
a.b.c.
37.Let with A in quadrant IV and with B in quadrant II and find:
a.b.c.
38.Prove the following identities:
a.
b.
c.
d.
39.If , and , express in terms of a trig function of .
40.Express as a single trig function and then simplify:
41.Solve for
42.Solve for
43.Solve for
44.Solve for
45.Solve for
46.Find all radian solutions for
47.In triangle ABC, , , and side meters. Find the missing parts of the triangle.
48.From a point on the ground, a person notices that a 100-ft antenna on the top of a hill subtends an angle of . If the angle of elevation to the bottom of the antenna is , find the height of the hill.
49.How many triangles ABC satisfy the following conditions? , ft., and meters
50.In triangle ABC, , cm, and cm. Find angle B.
51.In triangle ABC, if m, m, and m, find the measure of the smallest angle.
52.Two planes leave an airport at the same time. Their speeds are 360 mph and 420 mph and the angle between their courses is . How far apart are they after 1.5 hours?
53.Divide . Express your answer in the form .
54.Find x and y between 0 and so that is true.
55.Write in trigonometric form.
56.Write in standard form (use exact values).
57.Find . Express your answer in trigonometric form.
58.Divide: . Express your answer in standard form.
59.Find the three cube roots of .
60.Find all the solutions for the equation
61.A vector, V, has magnitude and forms an angle q with the positive x-axis. Find the magnitudes of and if = 850 and .
62.A ship heads east at a constant 15 mph. The current of the water is running due north at a constant 3 mph. Draw a vector, V, representing the true course of the ship.
63.Find the resulting equation when the parameter t is eliminated from the equations and .
64.Graph the curve described by the parametric equations and .
65.If W = 6i-8j and V = -2i-10j, then find V – W.
66.If V = 2i - 3j and U = i + j, then find the cosine of the angle between V and U.
67.Express the polar equation in rectangular form.
68.Write the pair in polar coordinates.
69,The graph of is a:
a)4-leaved rose
b)8-leaved rose
c)5-leaved rose
d)cardioid
70.Sketch the graph of .