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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-> 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.
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
