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

`(-(√(2) )/(2),-(√(2))/(2))`

Explanation:

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

The terminal side of
`-(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
`-(3\pi)/(4)` on the unit circle is given by

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

where
`\theta` is the reference angle for
`-(3\pi)/(4)` which is
`(\pi )/(4)`. See diagram in attachment.

Therefore the coordinates are;

`(-\cos((\pi )/(4)),-\sin((\pi )/(4)))`.

`(-(√(2) )/(2),-(√(2) )/(2))`