Name: ___________________________
Chapter 5 Functions Review
All of the problems with an asterisk are no calculator problems.
1) *Name the quadrants where tangent is negative. (A graph of the unit circle may help).
2) *In the second quadrant the sine of an angle is 0.5. What is the angle measure in radians and
the cosine of that angle?
3) *List all of the x-intercepts of f(x) = cos x.
4) Find the measures in degrees of a right triangle with sides of lengths 5, 12, and 13. Round to the
nearest degree.
5) Convert 250 degrees to radians and express your answer as a decimal rounded to the nearest
thousandth.
6) A 10 foot ladder leans against a vertical wall of a building. The foot of the ladder is 2.5 feet from
the base of the building. What angle does the ladder make with the ground? Round to the
nearest tenth of a degree.
7) *State the domain and range of f(x) = tan x.
8) *Convert 7π/3 into degrees and into revolutions.
9) *Sketch the graph of f(x) = sin x on the interval -3π/2 < x < 3π/2. Label key points.
10) Give all possible answers on the interval of 0 < x < 2π for the equation sin x = 3.25.
11) Suppose the sin θ = 0.87. Find the cos θ. Leave your answer in exact terms.
12) Triangle QRS has q = 12, r = 20, and Q = 35o. Find all possible values for the measure of angle R.
Round to the nearest tenth of a degree.
13) *If sin x < 0 and tan x < 0, then measured in degrees, x is between _____ and ______.
14) *If the point (1, 0) is rotated 150o with the origin as the center of rotation, what are the
coordinates of the image?
15) *Find the exact value of the cosine of 240o.
16) A circle has a radius of 4 inches. The central angle AOB has a measure of 150o. Find the area of
the sector. Do not round your answer and remember to label.
17) Find the angle with a measure closest to 1000 degrees whose cosine is 0.5.
18) Triangle DEF has d = 7cm, e = 12cm and f = 18cm. Find the measure of angle E rounded to the
nearest degree.
19) *What is the period of f(x) = tan x?
20) *Find all possible values for the tan x if we know the cos x =0.5.
21) *Name all places where f(x) = tan x is undefined.
22) The shortest side of a right triangle with an acute angle measuring 24 degrees has length 15cm.
Find the lengths of the other two sides. Round to the nearest tenth.
23) A circle has a central angle of 50o and a radius of 7 centimeters. Find the arc length in exact
terms.
24) Name three angle with positive measure in radians and three angles with negative measure in
radians whose tangent is -1.
25) *If the cos θ = 0.23 and 0 < θ < ∏/2, evaluate the following: sin (∏/2 – θ)
26) *Convert 225 degrees into radians and revolutions.
Answers
1) II, IV
2)
,
3)
or all odd multiples of
4) 23o, 67o, 90o
5)
6) 75.5o
7)
8) 420o = 7/6 revolutions
9)
1
-3π/2
-π
-π/2
π/2
π
3π/2
-1
10) There are no real answers because the sine cannot be larger than 1.
11)
12) m<R = 72.9o or 107.1o
13) 270o and 360o
14)
15)
1/2
16)
17) 1020o
18) 25o
19) Π radians or 180o
20)
21)
or all odd multiples of
22)
23)
24)
25) 0.23
26)
(any angles that fit into