Evaluate: \(\displaystyle{f{{\left({x}\right)}}}={\left({\cos{{x}}}-{\sin{{x}}}\right)}{\left({17}{\cos{{x}}}-{7}{\sin{{x}}}\right)}\)

Adolfo Hebert

Adolfo Hebert

Answered question

2022-04-05

Evaluate:
f(x)=(cosxsinx)(17cosx7sinx)

Answer & Explanation

Brennan Thompson

Brennan Thompson

Beginner2022-04-06Added 10 answers

you can do this without calculus. here is a way. i will use t for x we have
y=14+(costsint)(17cost7sint)
=14+17cos2t24sintcost+7sin2t
=14+172(1+cos2t)12sin2t+721cos2t
=26+5cos2t12sin2t
=26+13cos(2t+ϕ),  wherecosϕ=513,sinϕ=1213
so the maximum value of y is 39 and minimum value of y is 13.
therefore
13914+(costsint)(17cost7sint)3

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?