Download Sections 3.2.2, 3.2.3, 3.2.4 1. (a) √ 2 + / 3 2 , (b) √ 2 + / 2 2 2. (a) sin

Sections 3.2.2, 3.2.3, 3.2.4
p
p
√
√
2+ 3
2+ 2
1. (a)
,
(b)
2
2
√
3+2 2
=
,
(c) sin
2 s
6
√
x
3−2 2
cos
=
2
6
s
x
2. (a) sin(6θ), (b) cos(10x) (c) tan(14t)
3. (a)
LHS = sin(8x)
= sin(2(4x))
= 2 sin(4x) cos(4x) = RHS
6. (a) 2 sin(4x) cos(x)
(b) −2 sin(5x)
sin(−x)
= 2 sin(5x)5xsin(x)
5x
−3x
(c) 2 cos 2 sin 2 = −2 cos 2 sin
(b)
1
[sin(−x) + sin(5x)]
2
1
(b) [cos(2x) + cos(8x)]
2
(c) 4 [cos(−4x) − cos(6x)]
7. (a)
LHS = 1+sin(2x)
sin(2x)
1
= sin(2x)
+ sin(2x)
sin(2x)
= 2 sin(x)1 cos(x) + 1
1
1
= 21 sin(x)
+1
cos(x)
1
= 2 csc(x) sec(x) + 1 = RHS
8. (a) The equation is the same as :
2 sin2 (x) + sin(x) − 1 = 0,
The solution is: x = π6 + 2πn, x =
5π
+ 2πn, x = 3π
+ 2πn where n is any
6
2
integer.
(b) The equation is the same as:
(c)
LHS = sin(4x)
sin(x)
sin(2(2x))
= sin(x)
cos(2x)
= 2 sin(2x)
sin(x)
cos(x)) cos(2x)
= 2(2 sin(x)sin(x)
= 4 cos(x) cos(2x) = RHS
1 − cos(x)
= sin(x)
sin(x)
7
25
x
x
1
2
= √ , cos
=√
5. (a) sin
2
2
5
5
x
x
5
−1
(b) sin
= √ , cos
=√
2
2
26
26
which simplifies to
4. (a) −
cos(x)(cos(x) − 1) = 0
The solution is: x = π2 + πn, x = 2πn
where n is any integer.
15
3x
2