Question

prove that sin(270+theta)=(-cos theta)....

Answer 1

sin(180+90+ theta)
sin[180+(90+theta)]
we know sin(180+theta)= -sin(theta)
so here - sin (90+ theta)
again we know sin(90+ theta)= cos( theta)
so we have -sin (90+theta)= - cos( theta)

Answer 2

Answer:

Analytically, go like this :

sin(270-x) = sin(180+(90-x)),

We know sin(180+k) = -sin(k)

Here, k = (90-x),

sin(180+k) = -sin(90-x) = -cosx

Graphically,

Draw a circle of unit radius, suppose x be any angle say 30°.

Plot 30° & 270–30=240° on the circle.

cos30° will lie on x-axis & sin240° will also lie on x-axis. They will be same in magnitude but if considering sign convention, they'll lie on the opposite side of the y-axis. This makes one positive and the other negative.

Proved!

Hope this will help

Step-by-step explanation: