Question

Find the extreme values of

13cos x+3 root3sin x-4

Answer 1

Answer:

We know that maximum value of cosx and sinx is 1

so the maximum value of the given trigonometric

expression is when both sinx and cosx value are 1 respectively .

the maximum value of 13cosx + 3√3sinx - 4 is 13 (1) + 3√3(1) - 4 = 9 +3√3

we know that the minimum value of cosx and sinx is-1

so the maximum value of the given trigonometric expression is when both sinx and cosx value are -1 respectively.

the maximum value of 13cosx + 3√3sinx -4 is 13 (-1) + 3√3(-1) - 4 = -17 -3√3

so the range of expression 13cosx +3√3sinx -4 is-17 -3√3 to 9+ 3√3.

[ -17 -3√3 ,9+ 3√3]