Question

What are the coordinates of the point that corresponds to −3π/4 on the unit circle?

Answer 1

−3π/4

radians=degree*(pi/180)
degree=radians*180/pi
degree=-(3π/4)*180/π=3*180/4=-135°

-135°------------Quadrant II  (90°,180°)

we will define the X and Y Coordinate points on the Unit Circle
X2 + Y2 = r2 (Pythagorean Theorem)
r = Radius of the Circle = Hypotenuse of the Triangle 
135°-90°=45°
For Θ = 45°, we have X = 1*cos45° = √2/2 and Y = 1*sin45° = √2/2

for belonging to 2 quadrant
the X and Y Coordinate points
(-√2/2,√2/2)

Answer 2

Answer:

$(-\frac{\sqrt{2} }{2},-\frac{\sqrt{2}}{2})$

Step-by-step explanation:

The unit circle has the equation $\cos^2\theta+\sin^2\theta=1$.

The terminal side of  $-\frac{3\pi}{4}$ lies in the third quadrant.

In the third quadrant both the sine and the cosine ratios are negative.

The coordinates of the point that corresponds to  $-\frac{3\pi}{4}$ on the unit circle is given by

$(-\cos\theta,-\sin\theta)$.

where $\theta$ is the reference angle for $-\frac{3\pi}{4}$ which is $\frac{\pi }{4}$. See diagram in attachment.

Therefore the coordinates are;

$(-\cos(\frac{\pi }{4}),-\sin(\frac{\pi }{4}))$.

$(-\frac{\sqrt{2} }{2},-\frac{\sqrt{2} }{2})$