Question

Find the point on the terminal side of θ= -3pi/4 that has an x coordinate of -1. Show your work for full credit.

Answer 1

equilateral triangle, both sides have length 1

Answer 2

The (x,y) coordinates of points in polar form are (r cos(theta), r sin(theta)). Since we know the x coordinate of this point, we can use that to find r and then find the y coordinate using that value.

\[x = r \cos(\theta)\]
\[-1 = r \cos(-3 \pi / 4)\]
\[-1 = r \times (- \sqrt2 / 2)\]
\[r = \sqrt 2\]

Now that we know r, we find y = r sin(theta).

\[y = r \sin(\theta) = \sqrt 2 \times \sin(-3 \pi / 4) = -1\]

Answer 3

Thanks~