Question

A right triangle in which one acute angle is a reference angle for a 115 degree angle in standard position intersects the unit circle at (-0.423, 0.906). What is the approximate value of cos 115 degree?

Answer 1

`\cos (115\degree)=-0.423`

Explanation:

The parametric equations of a circle is

`x=r\cos \theta` and
`y=r\sin \theta`

The radius of the unit circle is 1 unit.

This implies that any point on the unit circle is represented by:

`x=\cos \theta` and
`y=\sin \theta`

where
`\theta` is the angle in standard position,

From the question, the given angle in standard position is
`115\degree`.

This angle intersects the unit circle at
`x=-0.423`

But
`x=\cos \theta`

We substitute
`\theta=115\degree` and
`x=-0.423`

This implies that:
`\cos (115\degree)=-0.423`