Math 1080: Section 5.5
Name___________________________________
Use an identity to write the expression as a single trigonometric function or as a single number.
1) sin 22.5° cos 22.5°
2)
2 tan 15°
1)
2)
1 - tan2 15°
3) 2 cos2 75° - 1
3)
4) sin 8x cos 8x
4)
5) cos24x - sin24x
5)
6) 1 - 2 sin2 2x
6)
Use identities to find the indicated value for each angle measure.
21
, cos > 0
Find cos(2 ).
7) sin =
29
5
,
<
13 2
8) cos
=-
9) tan
=
7
,
24
10) sin
=
4 3
, tan
7
11) cos 2 = -
<
<
<
2
<0
7
and <
9
2
<
7)
Find cos(2 ).
8)
Find sin(2 ).
9)
Find sin(2 ).
10)
Find sin .
11)
Express the function as a trigonometric function of x.
12) cos 4x
12)
13) sin 4x
13)
14) sin 3x
14)
15) tan 4x
15)
1
Verify that each equation is an identity.
1
16) cos4 x = (3 + 4 cos(2x) + cos (4x))
8
16)
17) cos(3x) = cos3 x - 3 sin2 x cos x
17)
18) sin(4u) = 2 sin(2u) cos(2u)
18)
19) cos(4u) = 2 cos2 (2u) - 1
19)
20) sin(4x) = (4 sin x cos x)(2 cos2 x - 1)
20)
21) sin3(3x) =
1
(sin(3x))(1 - cos(6x))
2
22) cos(4 ) = cos4
- 6 sin2
cos2
21)
+ sin4
22)
Write the product as a sum or difference of trigonometric functions.
23) 2 cos 6x cos 3x
24) 2 sin 2x sin 11x
23)
24)
Rewrite the following as a product of trigonometric functions.
25) cos 14° - cos 39°
26) sin (11t + 10) + sin (4t + 4)
25)
26)
Solve the problem.
27) Suppose that for an electrical appliance, voltage is given by V = 189 sin 120 t and
amperage by I = 1.07 sin 120 t, where t is time in seconds. Use identities to write the
wattage W = VI in the form W = a cos t + c.
2
27)