Question

solve for tan theta = 2sin theta

Answer 1

i got that far allready, but the answer in the back of the book is telling me 0, Pi, Pi/3, -Pi/3.

Answer 2

can you tell me what you did?

Answer 3

i have'nt done anything, only what you have done, i need to know how to continue the equation and find those values, i guess using the circle quadrant or something like that

Answer 4

2sinθ=2sinθcosθ ???

Answer 5

wooopppss..i looked at it wrongly; i thought it sin2x sorry

Answer 6

\[\tan(\theta) = 2\sin(\theta) \implies \frac{\sin(\theta)}{\cos(\theta)} = 2 \sin(\theta) \implies 2\cos(\theta) = 1\]

Answer 7

then \[ tan\theta = 2sin\theta => tan\theta - 2sin\theta\]
\[\frac{\sin\theta}{\cos\theta} -2\sin\theta = 0 => \frac{\sin\theta}{\cos\theta} - \frac{2\sin\theta*\cos\theta}{1*\cos\theta} = 0 \frac{\sin\theta-\sin2\theta}{\cos\theta} =0\]
lol, i went the long way woops.

Answer 8

\[\cos(\theta) = \frac{1}{2} \implies \cos(\theta ) = \cos(\frac{\pi}{3}) \implies \theta = 2 n \pi \pm \frac{\pi}{3}\]

Answer 9

tanθ=2sinθ
sinθ/cosθ=2sinθ
sinθ=2sinθcosθ
2sinθcosθ-sinθ=0
sinθ(2cosθ-1)=0
sinθ=0 or cosθ=1/2
so,
θ=0,pi and θ=pi/3 or -pi/3

Answer 10

Where \(n \in \mathbb{Z}\)..

Once can find all the solution by putting n = -2, -1 0, 1,2 etc etc.

I mean to say that integer values..

Answer 11

thanks very much that's right but how do i show that on the unit circle

Answer 12

abhiphardhu

Answer 13

@abhipardhu