Trigonometry Test 1 Practice
Chapters 1 and 2
NON-CALCULATOR PORTION
*** 4 Questions ***
1. Convert (a) 44
2. Convert (a)
2
5
(b) –120 to exact radians. (Give answer in terms of .)
(b)
3
to exact degrees.
2
3. Fill in the blanks in the following table using exact values.
'
sin
cos
tan
5
6
-405
5
units counter clockwise around a unit circle, starting at (1,0) and
3
finishing at point P. Find the coordinates of P, leaving the coordinates in exact form.
4. Suppose someone walks
Chapters 1 and 2
CALCULATOR PORTION
*** 10 Questions ***
5. Convert (a) 128o42/8//
(b) 12o6/23// to decimal degrees (to 3 decimal places).
6. Convert (a) 72.103o
second)
(b) 35.413o to degrees, minutes, and seconds (round to the nearest
7. Identify which quadrant the terminal side is in and find the angle of smallest positive measure
coterminal with (a) –942o
(b) 432o
8. Suppose = 10o is a central angle in a circle with radius is 4.0 cm. Recall that s = r
radians) and A = ½ r2 (angle in radians)
(a) Find the length of the arc cut by .
(b) Find the area of the circular sector formed by .
Given the point (x,
3
) on the unit circle with x
2
9. Solve for x. (Express answer in radical form.)
0:
10. Assuming s corresponds to this point, find tan s and sec s .
(angle in
Trigonometry Test 1 Practice
Find the exact value of the following:
11. sin
7
2
13. If sin s
3
4
12. cos
3
2
1
, find csc s and cot s .
2
and cos s
14. Find the exact value of each of the other five trigonometric functions for an angle
10
csc =
and cos > 0.
3
given
15. Find the exact value of x that satisfies the given conditions.
(a)
sin
1
,0<x<6
2
(b)
cos
2
,- <x<2
2
(c)
tan
3, 0 < x < 4
16. Use a calculator to find each to four decimal places.
(a)
csc 183 48'
(b)
sin 2.5
(c)
cos 3.8
(d)
tan 5
(e)
sec 10
(f)
cot –7
17. Solve the right triangle below.
A
c
b
39.72o
38.97
18. Simplify so that no quotients appear in the final expression using the fundamental identities.
csc sec
(a)
sin(-x)sec(-x)
(b)
cot u sin u
(c)
cot
Trigonometry Test 1 Practice
ANSWERS:
1.
2.
3.
11
45
(a) 72
11
45
(b) 270
(a)
(b)
'
5
6
6
-405
45
sin
1
2
1
,
2
8.
(a) s
1
2
tan s
1
12.
13.
2
2
3
3
1
2
(a) 128.702
(a) 72 6'11"
(a) II, 138
10.
11.
2
tan
3
5.
6.
7.
9.
3
2
2
4.
cos
(b) 12.106
(b) 35 24'47"
(b) I, 72
(b) A 1.396 cm 2
0.698 cm
3, sec s
2
2
2
csc s
2 3
, cot s
3
3
3
16.
17.
3 10
10
10
1
, cos
, tan
3, csc
, sec
10 , cot
10
10
3
3
7 11 19 23 31 35
7
2 5 8 11
,
,
,
,
,
, ,
,
,
,
(a)
(b)
(c)
6
6
6
6
6
6
4 4 4
3 3 3
3
(a) 15.0889 (b) 0.5985 (c) 0.7910 (d) 3.3805 (e) 1.1918 (f) 1.1475
A 50.28 , b 32.38, c 50.66
18.
(a)
14.
15.
sin
tan x
(b) cos u
(c) sec 2