Question

Angle 0 is drawn in standard position on the unit circle and intersects the unit circle at the point ( 3/10, y ) where y<0

1) in what quadrant does the terminal side of 0 lie? Justify awnsers

2) what is the value of y? Explain the Meath of you used to determine y

60 points

Answer 1

y ≈ - 0.954

Explanation:

(2). y² + x² = 1²

y² = 1 - x²

y² = 1 - (0.3)²

y² = 0.91

y = ± √0.91

y ≈ - 0.954

Answer 2

1. Quadrant IV
2. y ≈ -0.9539

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