# Need help solving a trig problem

• Feb 5th 2009, 02:27 PM
RaphaelB30
Need help solving a trig problem
Solve each equation for all θ in radians
sin θ = 1

π=Pie
• Feb 5th 2009, 04:03 PM
Amanda H
For $\displaystyle \sin \theta = 1$ there are an infinite number of solutions since the sine wave is continuous and is no restriction is set in the question. To find first you simply take the arcsin of 1:

$\displaystyle \theta = \arcsin 1$
$\displaystyle \theta = 1.57...$
which is equivalent to $\displaystyle \frac {\Pi}{2}$

The above answer is the only time the sine wave has a y value of 1 for $\displaystyle 0 \leq \theta \leq 2\Pi$. However the question asks for all values of $\displaystyle \theta$. For the rest of the solutions you add $\displaystyle \frac 2\Pi n$
Where n is any integer negative or positive. The 2$\displaystyle \Pi$ is used as the wave repeats every $\displaystyle 2\Pi$ and the n covers the fact that is repeats n times in a positive and negative direction.

Hope this helps you to understand it. If you need further explanation just ask.
• Feb 5th 2009, 04:06 PM
skeeter
Quote:

Originally Posted by RaphaelB30
Solve each equation for all θ in radians
sin θ = 1

π=Pie

you are expected to know that if $\displaystyle \sin{\theta} = 1$, then the primary value of $\displaystyle \theta = \frac{\pi}{2}$ , and repeats for values of $\displaystyle \frac{\pi}{2} + k \cdot 2\pi \, \, , \, \, k \in \mathbb{Z}$.

learn the unit circle ...

http://galileo.math.siu.edu/%7Emsull...unitcircle.gif

btw, this is pi ...

and this is pie ...

• Feb 5th 2009, 04:15 PM
RaphaelB30
Skeeter,
How did you know the primary value of the primary value of theta=pi/2.
• Feb 5th 2009, 04:20 PM
Amanda H
You might now arcsin as inverse sin?
You can get this value by drawing the sine wave, it is also the sort of value you should memorise and not need a calculator for.