Question

show me how to calculate -sin(3pi/4)

Answer 1

you want to get the reference angle, that is the first quadrant angle that has the same value, maybe varying only by sign

Answer 2

we know the sign is positive in the 2nd quadrant and in the first quadrant

Answer 3

of sine, that is

Answer 4

so this question is the exact same thing as -sin(3pi/4-pi/2)

Answer 5

which is -sin(pi/4)

Answer 6

think of the unit circle with radius 1, what would the y-value need to be with respect to the radius for theta to be pi/4?

Answer 7

So
\[-\sin\frac{3\pi}{4}=-\sin\frac{\pi}{4}=-\frac{\sqrt{2}}{2}\]