Question

How do I work out the least value of 15 cos x - 9 sin x as x varies?

Answer 1

write it as a single function of sine or cosine

Answer 2

\[a\cos(x)+b\sin(x)=r\sin(x+\theta)\]

Answer 3

\(r=\sqrt{a^2+b^2}\) and although you can find \(\theta\) if you want, it is unnecessary for this problem
you only need \(r\)

Answer 4

Okay, so then it is \[3\sqrt{34}\cos(x+a)\]

Answer 5

And so the smallest value of cos would be -1, so the least value would be \[-3\]

Answer 6

*-3 (sqr 34)

Answer 7

yes

Answer 8

\[-3\sqrt{34}\]

Answer 9

There

Answer 10

Cool, thanks, I got it. :)

Answer 11

yw