Question

Find tanx=3cosx for all answers from [0,2pi)

Answer 1

try writing tan x = sin x / cos x

Answer 2

Welcome!

Answer 3

sin x / cos x = 3 cos x
3 cos ^2 x = sin x

now use the identity cos^x = 1 - sin^2x

- substitute for cos^2 x
to get an equation only in sin x

Answer 4

I got the equation down to 3sin^2(x)+sin(x)-3=0 and used the quadratic equation. The result was( -1+- sqrt(37))/6. Does that seem correct?

Answer 5

so we get
3( 1 - sin^2 x 0 = sin x
3 - 3sin^2 x = sin x
3sin^2 x + sin x - 3 = 0

solve this

Answer 6

your equation was correct

Answer 7

Now that I have this answer, how would I put it in terms of pi/radian form?

Answer 8

yes that solution for sin x looks good

Answer 9

well work the values out on a calculator first
they come to 0.8471 and - 1.18

i would just give the answers as radians in decimal form
note that 2pi = 6.283

Answer 10

Thank you very much, this has been a huge help!

Answer 11

yw bro