Answer:
- Quadrant IV
- y ≈ -0.9539
Step-by-step explanation:
You want the quadrant of the terminal side, and the y-value associated with angle θ that intersects the unit circle where x = 3/10 and y < 0.
Quadrant
The quadrant in the coordinate plane where x > 0 and y < 0 is the 4th quadrant:
Quadrant IV
Y-value
A graphing program conveniently provides coordinates of the point of intersection of the line x = 3/10 with the unit circle. The y-value of that point is ...
y ≈ -0.9539
For some angle θ, points on the unit circle correspond to ...
(x, y) = (cos(θ), sin(θ))
Then angle θ will be an angle whose cosine is 3/10, and whose sine is negative.
We can find the y-value using trigonometry:
y = -sin(arccos(0.3))
y ≈ -0.9539
The Pythagorean theorem can be used to find the other leg of a right triangle with hypotenuse 1 and one leg 0.3.
y = -√(1 -0.3²) ≈ -0.9539
