Question

find the maximum value of 2sintheta-9sin2theta​

Answer 1

here is the answer

maximum value of 2sintheta-9sin2theta

when θ=π/2, y=1−4cos(π)+3sin(π)=1−4(−1)+0=1+4+0=5

When θ=0,y=1−4cos(0)+3sin(0)=−3.

But we can do better than that...y can be maximized a bit more, and we can do better on minimizing: y.. See if you can find a way to express y as a function of either cos or sin?

See arbautjc's trick in the comments above: when you have and expression which includes acos(2θ)+bsin(2θ) and can be expressed solely as a function of cos:

acos(2θ)+bsin(2θ)=a2+b2−−−−−−√cos(2θ−ϕ)

wherecosϕ=aa2+b2−−−−−−√ andsinϕ=ba2+b2−−−−−−√

Plotting the graph of y will always provide you with some intuition, as well.

marke me the brainlist mate