1. ## trig ratios

write each of the following as the ratios of positive acute angles.

in the examples i understand that $\displaystyle sin 330 = -sin 30$

but can someone please explain to me how it is that

$\displaystyle cos (3/4) \pi$= $\displaystyle -cos (1/4) \pi$

and $\displaystyle sin -(4/5) \pi$= $\displaystyle -sin (1/5) \pi$

i understand that $\displaystyle \pi$ = 180 but i am not geting it when i express each of the sectors in terms of $\displaystyle \pi$

2. Originally Posted by sigma1
write each of the following as the ratios of positive acute angles.

in the examples i understand that $\displaystyle sin 330 = -sin 30$

but can someone please explain to me how it is that

$\displaystyle cos (3/4) \pi$= $\displaystyle -cos (1/4) \pi$

and $\displaystyle sin -(4/5) \pi$= $\displaystyle -sin (1/5) \pi$

i understand that $\displaystyle \pi$ = 180 but i am not geting it when i express each of the sectors in terms of $\displaystyle \pi$
Hi sigma1,

$\displaystyle \cos \frac{3 \pi}{4}$ is a QII angle. Related angle is $\displaystyle \pi - \frac{3 \pi}{4}=\frac{\pi}{4}$.
Cosine is negative in the second quadrant.

$\displaystyle \cos \frac{\pi}{4}$ is a QI angle. Cosine is positive in the first quadrant.

Therefore, $\displaystyle \cos \frac{3 \pi}{4}=-\cos \frac{\pi}{4}$

The sin function is an odd function, meaning $\displaystyle \sin (-\theta)=-\sin \theta$

$\displaystyle \sin -\frac{4 \pi}{5}=-\sin \frac{4\pi}{5}$

Related angle is $\displaystyle \pi-\frac{4\pi}{5}=\frac{\pi}{5}$

$\displaystyle \sin \frac{4\pi}{5}$ is a QII angle. Sin is positive in the first and second quadrants.

Therefore, $\displaystyle \sin -\frac{4\pi}{5}=-\sin \frac{\pi}{5}$