Question

Use your calculator to find sin θ and cos θ if the point (9.31, 7.02) is on the terminal side of θ

Answer 1

Answer:

Part 1) $sin(\theta)=0.60$

Part 2) $cos(\theta)=0.80$

Step-by-step explanation:

Let

A(9.31, 7.02)

see the attached figure to better understand the problem

step 1

Find the value of r (hypotenuse of the right triangle)

Applying the Pythagorean Theorem

$r^2=x^2+y^2$

$r^2=9.31^2+7.02^2\\r^2=135.9565\\r=11.66$

step 2

Find the value of sin(θ)

In the right triangle of the figure

$sin(\theta)=\frac{y}{r}$ ----> by SOH (opposite side divided by the hypotenuse)

substitute

$sin(\theta)=\frac{7.02}{11.66}=0.60$

Is positive because lie in the First Quadrant

step 3

Find the value of cos(θ)

In the right triangle of the figure

$cos(\theta)=\frac{x}{r}$ ----> by CAH (adjacent side divided by the hypotenuse)

substitute

$cos(\theta)=\frac{9.31}{11.66}=0.80$

Is positive because lie in the First Quadrant