# yr11 2U trig

• Aug 26th 2009, 10:25 PM
deej813
yr11 2U trig
for 0<= θ <=360, solve (sin θ +1)(2cos θ -1)=0
• Aug 26th 2009, 10:35 PM
Chris L T521
Quote:

Originally Posted by deej813
for 0<= θ <=360, solve (sin θ +1)(2cos θ -1)=0

Applying the zero product property, we have either

$\sin\theta=-1$ or $\cos\theta=\tfrac{1}{2}$.

Can you take it from here?
• Aug 26th 2009, 10:50 PM
deej813
do i just put sin^-1(-1) in my calculator
and cos^-1(1/2)
??
sorry im very confused
• Aug 26th 2009, 11:09 PM
Chris L T521
Quote:

Originally Posted by deej813
do i just put sin^-1(-1) in my calculator
and cos^-1(1/2)
??
sorry im very confused

You could...but its best if you try to memorize these values from the unit circle: Unit circle - Wikipedia, the free encyclopedia

In our case, $\sin^{-1}\left(-1\right)$ has only one value in the specified interval for $\theta$, and its $\theta=270^{\circ}$

However, $\cos^{-1}\left(\tfrac{1}{2}\right)$ has two solutions in the given interval for $\theta$. They are $\theta_1=60^{\circ}$ and $\theta_2=300^{\circ}$.

Your final answer to the original question is all three values for $\theta$.

Does this make sense?
• Aug 26th 2009, 11:15 PM
deej813
yes i get it
finally :)
thanks