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

Answer:

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

Step-by-step 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: $\cos (115\degree)=-0.423$