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Practice Problems for Trig Quest
Algebra 2/Trigonometry
Name:
1) Solve, algebraically, for the exact values of  in the interval 0    2 : 2 cos  5 3  4 3
2) Solve for  , to the nearest minute, in the interval 0    360 : 3 tan 2   5 tan   2
3) Solve the equation in the interval 0    360 : 3 sin   3  2 cos 2 
4) Write this quadratic equation in standard form in terms of cos x: 4 cos 2 ( x)  4 cos(2 x)  1
7
3
and cos y  and x and y are positive acute angles, find
25
5
a. sin( x  y )
b) tan( x  y )
5) If sin x 
6) Write each expression as a single function or constant.
csc x
1  cos 2 
b. (sin  )(csc  )
c.
sec x
d. sin 2 x  cot 2 x  cos 2 x
Prove that the identities below are true.
7) cos x(tan x  sec x)  sin x  1
9)
8) sin 2  (1  tan 2  )  tan 2 
sin 2
 cos 2 
2 tan 
10) If
, and A is 0  A  45 , what is
? (Hint: Use the co-terminal identities on
the back of your blue reference sheet! Or remember: You can solve any equation by graphing the left and
right sides on your graphing calculator and finding the intersections!)
, and x is 0  x  45 , find
11) If
.
12) If the terminal side of and angle goes through the point ( 2 ,1) , find:
sin 
cos
csc
cot 
tan 
sec
13) Find the exact values of each expression below.
a)
d)
sin 60
sin
5
4
b)
e)
tan 60
sec
2
3
c)
f)
csc 45
cot
3
4
14) If tan  
5
and sin   0
12
b) Find (sin  )(tan  )
a) Find csc
15) Explain why cos 120 = -cos 60
16) Find the exact value of
17) If
tan  
sin 15 using the half angle identity.
12
and  is a positive acute angle, find cos 2 .
5
18) Multiple choice: Which of the following is equivalent to
a)
sin 
b)
 cos 
c)
sin( 90   ) :
cos 
19) If B  60, a  6, and c  10 , find the area of triangle ABC.
d)
 sin 
20) How many triangles can be created with these ingredients: T  50, t  20, and another side of
the triangle is 15.
21) In PQR , if p = 7, q = 9, and R  160 , find r to the nearest tenth.
22) In ABC , A  42 , C  58 , and c = 10. Find a to the nearest tenth.
23) In CBD, c  9, b  15, d  17. Find D . Round answer to the nearest minute.
24) From point A on one bank of a river, the angle of elevation to the top of a tree is 43 . As shown in
the figure below, point B is 100 feet behind A and in the same straight line as A and C. From B, the angle
of elevation to the top of the tree is 32 . Find the length of AC to the nearest foot.
25) Convert to radians. (Express radians in terms of  .)
a) 150
225
b)
26) Convert to degrees. (If necessary, round to the nearest tenth of a degree.)
a)
11
6
b)
5

27) Multiple choice: Find the exact value of f ( ) if f ( x)  2sin x  tan 5 x
3
(a) 
1
2
(b)  3
(c)  2 3
(d)  3
28) Identify the a) amplitude, b) frequency, c) period, d) phase shift, e) vertical shift, and f) range of the
function given.
1
y  3 cos( x)  1
2
a) amplitude:
b) frequency:
c) period:
d) phase shift:
e) vertical shift
f) range
29) Solve graphically the equation
sin 2x  3 cos x in the interval 0  x  2 .
30) A circular pie is cut into 12 equal pieces and each piece’s rounded edge of the crust is 3.2 inches
long. Find the radius of the pizza, rounded to the nearest tenth.
31) Write an equation that would create the curve below.
32) Two forces of 25 and 15 pounds act on a body so that the resultant is 32 pounds.
Find, to the nearest degree, the angle formed between the two forces.
33) The motion of a spring can be modeled by the equation y  1.6 cos( x)  5 where x represents the
number of seconds the spring is oscillating and y is the distance, in inches, of the spring from the ceiling.
Answer questions a-d below. (Note: To get credit for this question, you MUST clearly show and
document your work.)
a) How many seconds does it take for the spring to accomplish one full bounce (one cycle)?
b) How far is the spring from the ceiling at exactly 5 seconds?
c) If we let the spring bounce (assuming no friction) for 7 full seconds, how many times will it be at a
distance of 4.6 inches from the ceiling?