# Simple Trig Identity Question

• Sep 9th 2009, 06:15 PM
roflcoptur
Simple Trig Identity Question
I have basic knowledge of identities.

Solve each equation for theta if zero degrees is less than or equal to theta is less than or equal to 360 degrees.

1. 4sin theta - 3csc theta = 0
2. sec theta - 2tan theta = 0
• Sep 9th 2009, 08:02 PM
pacman
(1)4sin theta - 3csc theta = 0 --> 4 sin x - 3 csc x = 0;

4 sin x - 3(1/sin x) = 0,

(4 sin^2 x - 3)/sin x = 0,

4 sin^2 x - 3 = 0,

4 sin^2 x = 3,

sin^2 x - 3/4 = 0, factoring it.

(sin x + (sqrt 3)/2)(sin x - (sqrt 3)/2) = 0, the roots are

sin x = (sqrt 3)/2, -(sqrt 3)/2.

x = arcsin ((sqrt 3)/2, -(sqrt 3)/2)

x = {60, 120, 240, 300 degrees} or {pi/3, 2pi/3, 4pi/3, 5pi/3}
• Sep 9th 2009, 08:07 PM
pacman
4 sin x - 3 csc x = 0; for x = 0 to 360 degrees. The graph is shown below to check for the roots
• Sep 9th 2009, 10:02 PM
Hello roflcoptur
Quote:

Originally Posted by roflcoptur
...
2. sec theta - 2tan theta = 0

$\sec\theta -2\tan\theta=0$

$\Rightarrow \frac{1}{\cos\theta}-\frac{2\sin\theta}{\cos\theta}=0$

$\Rightarrow \frac{1-2\sin\theta}{\cos\theta}=0$

$\Rightarrow 1-2\sin\theta=0$

$\Rightarrow \sin\theta = \tfrac12$

$\Rightarrow \theta = 30^o, 150^o$