# Math Help - Trigonometry quest.

1. ## Trigonometry quest.

Hello.

a- Express 5sinx+ 12cosx in the form Rsin(x+A)

a- Find the Maximum and Minimum values of f(x) where
f(x)= 1 / ( 5sinx+12cosx+17). State also the values of x in the range of x is greater than 0 less than 360 degrees, at which they occur.

I can do part a) My answer is 13sin(x+67,4)
But i cant do part b)

Thanks.

2. Originally Posted by Oasis1993
Hello.

a- Express 5sinx+ 12cosx in the form Rsin(x+A)

a- Find the Maximum and Minimum values of f(x) where
f(x)= 1 / ( 5sinx+12cosx+17). State also the values of x in the range of x is greater than 0 less than 360 degrees, at which they occur.

I can do part a) My answer is 13sin(x+67,4)
But i cant do part b)

Thanks.
HI

your first part is correct .

(b) $\frac{1}{5\sin x+12\cos x+17}=\frac{1}{13\sin (x+67.4^o)+17}$

Note that sin is max and min at 1 and -1 respectively .

For f(x) to be max , its denominator has to be min and vice versa .

You can also find the corresponding value of x , depending whether you are taking 1 or -1 for your sin .