Question

Evaluate sin 315º without using a calculator.O A. 132DIRO B.B. -12OC, V22O D. - 12

Answer 1

Choice D.

Step-by-step explanation:

Another way to write 315 degrees is

`315-360=-45`

In other words, when measured clockwise, 315 degrees = -45 degrees; therefore, our problem becomes

`\sin 315^o=\sin -45^o`

since

`\sin \theta=-\sin -\theta`
`\sin 45=-\sin -45`
`\frac{\sqrt[]{2}}{2}=-\sin -45`
`\sin -45=-\frac{\sqrt[]{2}}{2}`

Therefore,

`\boxed{\sin 315^o=-\frac{\sqrt[]{2}}{2}}`

which is our answer!