Question

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

Answer 1

\[\sin 5\pi \div 4\]

Answer 2

is the 4 inside the sin?

\[\sin(\frac{ \pi }{ 4 }) \]
or this?
\[\frac{ \sin(\pi) }{ 4 }\]

either way, without a calculator, you can use the unit circle to determine the sin



clickable: https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/300px-Unit_circle_angles_color.svg.png

simply find the angle you need, then look at the second coordinate within the parentheses

Answer 3

So then it would be positive?

Answer 4

yup, if it's sin(pi/4) then it's positive

Answer 5

Thank you!