Question

Someone please help!!!!!! trigonometry- trig equations!!!

Answer 1

1. 0, 2 π , π , 2 π/3 , 4 π/3

2. 7 π/6 , 11 π/6

Explanation:

1. we want to find the value of theta

Let us represent theta by x for ease of documentation

So we have ;

sin 2x + sin x = 0

Mathematically;

sin 2x = 2sinxcosx

So;

2 sin x cos x + sin x = 0

sin x (2 cos x + 1) = 0

sin x = 0

or

2cos x + 1 = 0

x = arc sin (0)

within the given range;

x = theta = 0 , 2 π , π

For;

2 cos x + 1 = 0

2cos x = -1

cos x = -1/2

cos x = -0.5

x = arc cos (-0.5)

x = 2 π/3 , 4 π/3

2. cos 2 x = 1 + sin x

Mathematically;

cos 2 x = 1-2 sin^2x

let sin x = y

1-2y^2 = 1 + y

y = -2y^2

1 = -2y

y = -1/2

y = -0.5

sin x = y

sin x = -0.5

x = arc sin (-0.5)

x = 7 π/6 , 11 π/6