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?

Respuesta :

Answer:

[tex]\cos (115\degree)=-0.423[/tex]

Step-by-step explanation:

The parametric equations of a circle is

[tex]x=r\cos \theta[/tex] and [tex]y=r\sin \theta[/tex]

The radius of the unit circle is 1 unit.

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

[tex]x=\cos \theta[/tex] and [tex]y=\sin \theta[/tex]

where [tex]\theta[/tex] is the angle in standard position,

From the question, the given angle in standard position is [tex]115\degree[/tex].

This angle intersects the unit circle at [tex]x=-0.423[/tex]

But [tex]x=\cos \theta[/tex]

We substitute [tex]\theta=115\degree[/tex] and [tex]x=-0.423[/tex]

This implies that: [tex]\cos (115\degree)=-0.423[/tex]