# Trigonometric equations

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• Apr 22nd 2010, 05:47 AM
coobe
Trigonometric equations
Hello ! I cant remember how to solve this... please help me :)

Find all the solutions in the intervall [-4pi; 4pi] for

a) sin(x) = 0.23
b) cos(x) = -0.9
c) tan(x) < 1
• Apr 22nd 2010, 04:10 PM
skeeter
Quote:

Originally Posted by coobe
Hello ! I cant remember how to solve this... please help me :)

Find all the solutions in the intervall [-4pi; 4pi] for

a) sin(x) = 0.23
b) cos(x) = -0.9
c) tan(x) < 1

(a) solutions are in quads I and II

going from $\displaystyle 0$ to $\displaystyle 4\pi$ ...

$\displaystyle x = \arcsin(.23)$ , $\displaystyle \pi - \arcsin(.23)$ , $\displaystyle 2\pi + \arcsin(.23)$ , $\displaystyle 3\pi - \arcsin(.23)$

.. now you go from $\displaystyle 0$ to $\displaystyle -4\pi$

(b) solutions are in quads II and III

from $\displaystyle 0$ to $\displaystyle 4\pi$ ...

$\displaystyle x = \arccos(-0.9)$ , $\displaystyle 2\pi - \arccos(-0.9)$ , $\displaystyle 2\pi + \arccos(-0.9)$ , $\displaystyle 4\pi - \arccos(-0.9)$

get the idea?

for (c) , look at the graph.