Question

Consider the right triangle shown below that has an interior angle measure of θ radians.Use the slider in the applet above to show a circle centered at the left-most vertex of the triangle.Consider the terminal point P.What is the measure of the terminal point's vertical distance above the center of the circle in units of the radius of the circle?   What is the value of sin(θ)?sin(θ)=Consider the terminal point P.What is the measure of the terminal point's horizontal distance to the right of the center of the circle in units of the radius of the circle?   What is the value of cos(theta)?cos(θ)=

Answer 1

Given

Graph

Procedure

b.

i)

$\frac{1.93}{2.5}=0.772$

ii)

$\begin{gathered} \sin \theta=\frac{1.93}{2.5} \\ \sin \theta=0.772 \end{gathered}$

c.

i)

$\frac{1.59}{2.5}=0.636$

ii)

$\begin{gathered} \cos \theta=\frac{1.59}{2.5} \\ \cos \theta=0.636 \end{gathered}$