Question

Find two solutions of the equation. Give your answers in degrees ( 0^o ≤ θ < 360^o ) and in radians

( 0 ≤ θ < 2π ).Do not use a calculator.

(a) sin θ = 1/2                         (b) sin θ = - 1/2

Answer 1

Step 1:

(b)

The expression is  .

The general solution of sine function is  .

  where  .

Substitute in the above expression.

Substitute in the above expression.

The value of  in degrees is .

Substitute in the above expression.

The value of  in degrees is .

The solution of is not in the interval , hence it is not considered.

The solutions of x are and  .

Comments

Step 2:

The general solution of sin function is  .

  where  .

Substitute in the expression.

Substitute in the expression.

Substitute in the expression.

The solution of is not in the interval  , hence it is not considered.

The solutions of x are and  .

Solution:

The solutions of x are  and  .

The solutions of x are and  .

Answer 2

Step 1:

(a)

The equation is  .

The general solution of sine function is  .

  where  .

Substitute in the expression.

Substitute in the expression.

  

The value of  in degrees is .

The solutions of x are and  .

Step 2:

The equation is  .

The general solution of sin function is  .

  where  .

Substitute in the expression.

Substitute in the expression.

The solutions of x are and  .

Solution:

(a) The solutions of x are and  .

The solutions of x are and  .