Math 1080: Section 5.3
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Use Identities to find the exact value.
1) cos -75°
1)
2) cos 165°
2)
3) cos 255°
3)
4) cos
4)
5) cos
12
19
12
5)
6) cos 36° cos 24° - sin 36° sin 24°
6)
7
5
7
5
cos
+ sin
sin
12
12
12
12
7)
7) cos
Use the cofunction identities to find an angle
8) tan = cot (30°+ 5 )
that makes the statement true.
9) sin (3 - 17°) = cos ( + 43°)
10) sin
8)
9)
= cos (4 + 60°)
10)
11) tan (2 - 140°) = cot ( + 5°)
11)
12) cot 5 = tan 4
12)
13) sec (6 + 17°) = csc (2 - 7°)
13)
14) sin ( + 4°) = cos ( + 6°)
14)
15) cot (2 - 20°) = tan ( - 10°)
15)
Use identities to write each expression as a function of .
16) cos ( - )
17) cos
+
16)
17)
2
1
18) cos ( + 270°)
18)
Find the exact value of the expression using the provided information.
1
1
19) Find cos(s + t) given that cos s = , with s in quadrant I, and sin t = - , with t in quadrant
3
2
19)
IV.
20) Find cos(s + t) given that sin s = -
1
1
, with s in quadrant IV, and sin t = , with t in
2
4
20)
quadrant II.
21) Find cos(s + t) given that cos s =
1
1
, with s in quadrant I, and sin t = , with t in quadrant II.
3
4
22) Find cos(s - t) given that cos s = -
21)
12
8
, with s in quadrant II, and sin t =
, with t in
13
17
22)
1
3
, with s in quadrant III, and cos t = - , with t in
2
5
23)
3
5
, with s in quadrant IV, and sin t = , with t in
3
6
24)
quadrant II.
23) Find cos(s - t) given that cos s = quadrant III.
24) Find cos(s - t) given that sin s = quadrant IV.
Verify that the equation is an identity.
3
1
=
cos x - sin x
25) cos x +
6
2
2
26) cos
27) sec
28)
2
2
25)
- x = -sin x
26)
+ x = -csc x
cos( + )
= cot
cos sin
27)
- tan
28)
29) cos(x - y) - cos(x + y) = 2 sin x sin y
30)
29)
cos(x - y) 1 + tan x tan y
=
cos(x + y) 1 - tan x tan y
30)
2
Solve the problem.
31) The output voltage of a generator is given by V = 162 cos 2 ft -
. Express the voltage as
31)
32) A vibrating wire has a vertical displacement given by y = 9(cos 2 x cos bt + sin 2 x sin bt).
Assume b and t are constants. Write y as a cosine function of x.
32)
33) In a particular situation, the pressure, P, exerted on a person's eardrum at a distance of 9
a
feet from the source is given by the function: P(t) = cos (2n - ct) , where n is a positive
9
33)
6
the sum of a sine and a cosine function.
integer. Use the difference identity for cosine to simplify P in this situation.
3