Question

PLEASE HELP ASAP WILL MARK BRAINLIEST

Answer 1

Answer:

$\sin \frac{3\pi}{2} = -1$

$\cos\frac{3\pi}{2} =0$

Step-by-step explanation:

Please refer to the image attached.

Here we have a circle with unit radius. At some angle Ф the radius = 1 , and it is the hypotenuse (shown by green line in the image attached) of the ΔPQR thus formed. As our angle  Ф increases, the hypotenuse gets closer to the positive y axis and at 90°, it overlap the y axis. Hypotenuse (H) and Opposite site (O) becomes same and Adjacent (A) becomes 0.

As our angle move further and reaches 180, the Hypotenuse and adjacent becomes same and overlap negative x axis. As we move further at 270 i.e $\frac{3\pi}{2}$ , the hypotenuse and opposite side overlap on y axis and Adjacent side become 0. However the opposite side becomes negative here .

Our sine ratio says

$\sin \frac{3\pi}{2} =\frac{opposite}{Hypotenuse}$

$\sin \frac{3\pi}{2} =\frac{-1}{1}$

$\sin \frac{3\pi}{2} =-1$

Hence we have our $\sin \frac{3\pi}{2} = -1$

Now

$\cos\frac{3\pi}{2} =\frac{Adjacent}{Hypotenuse}$

Adjacent as we discussed is 0 at $\frac{3\pi}{2}$

$\cos\frac{3\pi}{2} =\frac{0}{1}$

$\cos\frac{3\pi}{2} =0$