Question

Find the range of 13cosx+3root3sinx-4

Answer 1

we know that maximum value of cosx and sinx is 1

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

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

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

⇒ [-17 -3√3 , 9 + 3√3]