Question

find the value of sine and cosine for the following drawing of a unit circle.\\(\theta = 1.77\pi\\) rad\\((0.75, -0.66)\\)\\(\sin(\theta) =\\)\\(\cos(\theta) =\\)

Explanation:

Step1: Recall unit circle coordinates

On a unit circle, the coordinates of a point corresponding to an angle \(\theta\) are \((\cos(\theta), \sin(\theta))\).

Step2: Identify the coordinates

From the given unit circle drawing, the point is \((0.75, -0.66)\). So, by the definition of unit circle coordinates, \(\cos(\theta)\) is the x - coordinate and \(\sin(\theta)\) is the y - coordinate.

Answer:

\(\sin(\theta)= - 0.66\)
\(\cos(\theta)=0.75\)