15. Find all solutions in the interval (0,2) (a) — sin(20) = (b) - 3 cos(2x)...

Question

Question

15. Find all solutions in the interval (0,2) (a) — sin(20) = (b) - 3 cos(2x) - 0.8 - 0

Answer 1

Answer #1

a) 2/3 Sin2x = 1/4

》 Sin2x = 3/8 = 0.375

Using a calculator, we find that the value of SinQ = 0.375 when Q = 22.02°

That is 2x = 22.02

Since the range is between 0 to 2pi, we'll also consider the second quadrant where the value of Q will be 180 - 22.02 = 157.98°

Therefore 2x = 22.02° or 157.98°

》 x = 11.01° or 78.99°

b) -3 Cos2x - 0.8 = 0

》 -3 Cos2x = 0.8

Cos2x = 0.8/-3

Cos2x = -0.27

Since the value is negative, 2x will lie in the second or the third quadrant.

Using a calculator, we find that CosQ = 0.27 when Q = 74.33°

In the second and third quadrant,

2x = 105.67° or 254.33°

x = 52.835 or 127.165

Answer 2

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