Finding angle/ Double angle formula

**cam_ddrt** · May 29th 2009, 06:35 AM

I am studying for a test and cannot figure out how to do these two questions.

1. Find the angle,θ, between the positive x-axis and a line segment joining the origin and a variable point (x, x²+1) on the graph of y=x²+1

2. Using the double angle formula sin2θ=2sinθcosθ find all θ, 0<θ<2pi,
such that sin2θ=sinθ

Thanks!

**Isosceles Kramer** · May 29th 2009, 07:04 AM

For the first one draw the diagram.
Then create the right triangle of base $x$ and height $x^2+1$ .
Now, $\tan{\theta}=\frac{x^2+1}{x}$ .
That's pretty much all there is to it.

Number 2 is just simple substitution.

$\sin{2\theta}=\sin{\theta}$
$2\sin{\theta}\cos{\theta}=\sin{\theta}$
$2\cos{\theta}=1$
$\cos{\theta}=\frac{1}{2}$

**e^(i*pi)** · May 29th 2009, 07:43 AM

Originally Posted by Isosceles Kramer

For the first one draw the diagram.
Then create the right triangle of base $x$ and height $x^2+1$ .
Now, $\tan{\theta}=\frac{x^2+1}{x}$ .
That's pretty much all there is to it.

Number 2 is just simple substitution.

$\sin{2\theta}=\sin{\theta}$
$2\sin{\theta}\cos{\theta}=\sin{\theta}$
$2\cos{\theta}=1$
$\cos{\theta}=\frac{1}{2}$

Number 2 should be solved via factoring in order to get all the solutions:

$2sin{\theta}cos{\theta} - sin{\theta} = 0$

$sin{\theta}(2cos{\theta}-1) = 0$

$sin{\theta} = 0 \text { or } cos{\theta} = \frac{1}{2}$

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