Solve for sin, cos, and tan

Question

1. Solve: 2 sin x =-1

 

2. Solve: 4cos² x=1

 

3. Solve: 3 tan x= √3

Answer 1

 

1)

 

2sinx = 1

 

 

Divide both sides of the equation by 2.

 

sinx = -1/2

 

x = 30

 

 

sine is negative in the 3rd and 4th quadrants.

 

x = 180 + 30 = 210

x = 360 - 30 = 330

 

 

2)

 

4cos²(x) = 1

 

 

Divide both sides of the equation by 4.

 

cos²x = 1/4

 

(cosx)² = 1/4

 

 

Square-root both sides of the equation.

 

cosx = 1/2

 

 

x = 60

 

 

cosine is positive in the first and 4th quadrant.

 

x = 360 - 60 = 300

 

 

3)

 

3tan x = √3

 

 

Divide both sides of the equation by 3.

 

tan x = √(3) / 3

 

x = 30

 

 

tangent is positive in the 3rd quadrant.

 

x = 180 + 30

x = 210