SOLUTION: Point A = (cosθ,sinθ) is at the intersection of x2 +y2 = 1 and a ray starting at the origin that makes an angle, θ, with the positive x-axis. The ray starting at the origin thro

SOLUTION: Point A = (cosθ,sinθ) is at the intersection of x2 +y2 = 1 and a ray starting at the origin that makes an angle, θ, with the positive x-axis. The ray starting at the origin thro

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Question 1163606: Point A = (cosθ,sinθ) is at the intersection of x2 +y2 = 1 and a ray starting at the origin that makes an angle, θ, with the positive x-axis. The ray starting at the origin through point P, which is on x2 +y2 = 1,makes an angle of 2θ with the positive x-axis.
(a) Explain why P = (cos 2θ, sin 2θ).
(b) Reflect B = (1,0) over the line CA to get an equivalent
form of the coordinates of P written in terms of cos θ and sin θ. C is the origin.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The measure of CA and CP are each 1.

is the measure of CD divided by the measure of CA, or just CD, hence the

coordinate of point A is

. Similarly, the measure of AD and therefore

is the

-coordinate of A.

Using the same rationale it is elementary to show that the coordinates of P are

.

I'm still working on writing out the rest. Send me a note and I'll send it back perhaps tonight or tomorrow AM.

John

My calculator said it, I believe it, that settles it

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