Question

on the unit circle, sketch ( \theta = 0.85pi ) radians in standard position. then use the coordinates shown, which are rounded to the hundredths place, to find ( cos(0.85pi) ) and ( sin(0.85pi) ). write your answers to the hundredths place.

Explanation:

Step1: Recall the unit - circle definitions

On the unit circle \(x = \cos\theta\) and \(y=\sin\theta\), where \((x,y)\) is the point on the unit circle corresponding to the angle \(\theta\) in standard position.

Step2: Calculate the angle value

We know that \(\theta = 0.85\pi\approx0.85\times3.14 = 2.669\) radians.
Using a calculator (in radian mode):
\(\cos(0.85\pi)\approx - 0.66\)
\(\sin(0.85\pi)\approx0.75\)

Answer:

\(\cos(0.85\pi)=- 0.66\)
\(\sin(0.85\pi)=0.75\)