Trig Sem Final Ch. 5
Name___________________________________
Perform the indicated operations and simplify the result so there are no quotients.
(sin θ + cos θ)2
1)
1 + 2 sin θ cos θ
1)
2) sec θ sin θ - 1
2)
3) sin θ + cos θ
3)
tan θ
cos θ
sin θ
Use Identities to find the exact value.
4) cos - 7"
12
4)
5) cos "
5)
12
1
Find the exact value of the expression using the provided information.
6) Find cos(s + t) given that sin s = - 1 , with s in quadrant IV, and sin t = 1 , with t in
2
4
6)
quadrant II.
Use identities to find the indicated value for each angle measure.
7) cos 2θ = - 3 and " < θ < "
Find sin θ.
8
2
8) sin θ = - 4 , 3" < θ < 2"
5
2
7)
8)
Find cos(2θ).
Use an identity to write the expression as a single trigonometric function or as a single number.
9) 2 tan 15°
1 - tan 2 15°
9)
10) cos24x - sin 24x
10)
11) 2 tan 30°
11)
1 - tan 2 30°
2
Use the fundamental identities to find the value of the trigonometric function.
12) Find tan θ if cos θ = 1 and θ is in quadrant IV.
2
13) Find cot θ if tan θ =
14) Find sin θ if cos θ = -
3
7 and θ is in quadrant III.
13)
11 and θ is in quadrant III.
6
14)
15) Find sin θ if cot θ = - 2 and cos θ < 0.
15)
Determine all solutions of the equation in radians.
16) Find sin θ , given that cos θ = 1 and θ terminates in 0 < θ < 90°.
2
4
17) Find sin x , given that sin x = 1 and x terminates in 0 < x < " .
2
12)
4
2
Find the exact value by using a half-angle identity.
18) sin 165°
16)
17)
18)
3
Use a sum or difference identity to find the exact value.
19) sin 7" cos " - cos 7" sin "
24
8
24
8
19)
20) tan 25° + tan 5°
20)
21) tan 170° - tan 50°
21)
22) tan 7"
22)
23) sin 25° cos 35° + cos 25° sin 35°
23)
1 - tan 25° tan 5°
1 + tan 170° tan 50°
12
Find the exact value of the expression using the provided information.
24) Find sin(s + t) given that cos s = - 1 , with s in quadrant III, and cos t = - 3 , with t in
4
5
24)
quadrant III.
25) Find tan(s + t) given that sin s = 1 , with s in quadrant II, and sin t = - 1 , with t in
4
2
25)
quadrant IV.
Write in terms of the cofunction of a complementary angle.
26) tan 123°20′
27) sin "
26)
27)
17
4
Use the cofunction identities to find an angle θ that makes the statement true.
28) tan θ = cot (30°+ 5θ)
Using a sum or difference identity, write the following as an expression involving functions of x.
29) tan x - "
3
Complete the sentence so the result is an identity. Let x be any real number.
30) sin x = ( )(cos x)
31)
+ sin 2x = 1
28)
29)
30)
31)
Use the fundamental identities to simplify the expression.
32) tan θ
cot θ
32)
33) tan θ
33)
2
34) 1 + tan x
34)
sec θ
sec x
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
1 + tan 2 x
35)
35)
sec x
Decide whether the expression is or is not an identity.
36) 1 - cos2x = 1 - cos x
36)
Use a graphing calculator to make a conjecture as to whether each equation is an identity.
37) cos 2x = 2cos2x - 1
37)
5
Answer Key
Testname: TRIG SEM FINAL CH5
1) 1
2) 0
3) sec θ csc θ
4)
24
6
5)
6+
4
2
6) 1 - 3 5
8
7) sin θ =
11
4
8) - 7
25
3
9)
3
10) cos 8x
11) 3
12) - 3
13) 3 7
7
14) - 5
6
5
15)
5
6
16)
4
8-2
4
17)
18) 1
2-
2
15
3
19) 1
2
20)
3
3
21) - 3
22) -2 - 3
23)
3
2
24) 3 15 + 4
20
6
Answer Key
Testname: TRIG SEM FINAL CH5
25) 4 3 +
15
-11
′
26) cot -33°20
27) cos 15"
34
28) θ = 10°
29) tan x 1+
3
3 tan x
30) tan x
31) cos2x
32) tan2θ
33) sin θ
34) sec x
35) sec x
36) Not an identity
37) Identity
7