Question

Determine the sign of sin five pi divided by four without using a calculator.

Answer 1

Imagine the unit circle.


`\pi \ \textless \ (5\pi)/(4) \ \textless \ 2\pi`

Therefore, the point will be below the x axis, so its y coordinate will be negative.

Therefore, the sign is negative.

Answer 2

Negative

Explanation:

Given is an angle 5pi/4 and we have to find sine value

Since 5pi/4 lies in III quadrant using All silver tea cups rule, sine will be negative.

Principal value for

`(5\pi)/(4) is (\pi)/(4)`

Hence sin
`=(5\pi)/(4) =(-1)/(√(2) )`