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Trigonometric Equations with Reciprocal Functions

The reciprocal trigonometric functions areandGiven an equation of this sort we find the value oforfirst, then find the reciprocal of this to find the value oforthen solve this or these equation using the normal method for finding multiple angles of trigonometric formulae.

Example: Solve the formulafinding all solutions 0-360 degrees.

The expression factorises into

We follow the normal rule for quadratics by setting each factor equal to 0 and solving.

and

There are no other solutions in the range 0 – 360 degrees.

Example: Solve the formulafinding all solutions 0-360 degrees.

The expression factorises into

We follow the normal rule for quadratics by setting each factor equal to 0 and solving.

andand

and

Example: Solve the equationin the range 0 – 360 degrees.

or

or

oror

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