# Trigonometric equations

• April 22nd 2010, 05:47 AM
coobe
Trigonometric equations

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

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

Originally Posted by coobe

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 $0$ to $4\pi$ ...

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

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

(b) solutions are in quads II and III

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

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

get the idea?

for (c) , look at the graph.