Question

HELP DUE TODAY!!!!!!!!!

. Write the (x, y) coordinates for P in terms of cosine and sin.
6. Using the image above, if cos(Θ) = 0.6, what are the coordinates of P? Explain your reasoning.

Answer 1

Answer: (0.6, -0.8)

Step-by-step explanation:

Use the pythagorean trig identity to determine sine based on cos(theta) = 0.6

`\sin^2(\theta)+\cos^2(\theta) = 1\\\\\sin^2(\theta)=1-\cos^2(\theta)\\\\\sin(\theta)=\pm√(1-\cos^2(\theta))\\\\\sin(\theta)=-√(1-\cos^2(\theta)) \ \ \text{....sine is negative in quadrant Q4}\\\\\sin(\theta)=-√(1-(0.6)^2)\\\\\sin(\theta)=-√(1-0.36)\\\\\sin(\theta)=-√(0.64)\\\\\sin(\theta)=-0.8\\\\`

Since
`\cos(\theta)=0.6 \text{ and } \sin(\theta)=-0.8`, the location of point P is (0.6, -0.8)

Recall that for any point (x,y) on the unit circle, we have:

`\text{x}=\cos(\theta)\\\\\text{y}=\sin(\theta)`

meaning cosine is listed first in any (x,y) pairing.