Problem with a trigonometric equation.

[Shawn Garsed]

Homework Statement

Which of the following is not a possible solution of
0=sinθ+cosθtan^2θ?

A. 3pi/4
B. 7pi/4
C. 2pi
D. 5pi/2

Homework Equations

All trigonometric identities.

The Attempt at a Solution

Too much to write down, at least two pages long, but I've been trying to rewrite the equation so that there's only one trigonometric function left. I would really like a push in the right direction.

 

[tiny-tim]

Hi Shawn!

(have a pi: π and try using the X² icon just above the Reply box )

… I've been trying to rewrite the equation so that there's only one trigonometric function left. I would really like a push in the right direction.

I'm not sure what you mean by that,

but wouldn't it be easier to factor it, in the form f(θ)g(θ) = 0, so that you can then solve (or in this case, check) the easier equations f(θ) = 0 and g(θ) - 0 separately?

 

[Shawn Garsed]

I think I got it:

sinθ+cosθtan²θ=sinθ(1+tanθ), therefore θ=0, 180, 135 or 315, which means 5π/2 is not a possible solution.

 

[tiny-tim]

I think I got it:

sinθ+cosθtan²θ=sinθ(1+tanθ), therefore θ=0, 180, 135 or 315, which means 5π/2 is not a possible solution.

Perfect!

(except technically you needed to go above 360°, since 5π/2 > 2π )