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# Trigonometry Examples

,

Take the inverse sine of both sides of the equation to extract from inside the sine.

and

The exact value of is .

and

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.

and

Subtract from .

and

Find the period.

The period of the function can be calculated using .

and

Replace with in the formula for period.

and

Solve the equation.

The absolute value is the distance between a number and zero. The distance between and is .

and

Divide by .

and

and

and

The period of the function is so values will repeat every radians in both directions.

and

Consolidate the answers.

and

and

Take the inverse cosine of both sides of the equation to extract from inside the cosine.

and

The exact value of is .

and

The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.

Simplify .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Find the period.

The period of the function can be calculated using .

and

Replace with in the formula for period.

and

Solve the equation.

The absolute value is the distance between a number and zero. The distance between and is .

and

Divide by .

and

and

and

The period of the function is so values will repeat every radians in both directions.

, for any integer

Consolidate the answers.

, for any integer

, for any integer