Question

Hi, can you help me to rewrite the six trigonometric functions of theta in terms of sine and/or cosine of the reference angle Sketch both the given angle and reference angle on the circle.

Answer 1

We want to find the six trig functions of the angle given in terms of that of its reference angle.

`\theta=(7\pi)/(9)`

This is a sketch of the angle;

This is smaller that 360, so it cant be reduced further, It is the reference angle.

So;

`\begin{gathered} \sin \theta=\sin (7\pi)/(9) \\ \cos \theta=\cos (7\pi)/(9) \\ \tan \theta=(\sin (7\pi)/(9))/(\cos (7\pi)/(9)) \\ \csc \theta=(1)/(\sin (7\pi)/(9)) \\ \sec \theta=(1)/(\cos (7\pi)/(9)) \\ \cot \theta=(1)/(\tan\theta)=(\cos (7\pi)/(9))/(\sin (7\pi)/(9)) \end{gathered}`

These are our trigonometric ratios.