# Thread: trig, minimum value?

1. ## trig, minimum value?

(a) Show that 3sin3θ−4cos3θ can be written in the form Rsin(3θ−α), with R>0 and 0<α<90°.

(b) Deduce the minimum value of 3sin3θ−4cos3θ and work out the smallest positive value of θ (to the nearest 0.1°) at which it occurs.

I did the first part and got $\displaystyle 5sin( 3\theta-53.1)$

but how do I find the minimum value? I have set it equal to 0, but that does not give me the correct answer.

can someone please tell me
?

Thanks!

2. Originally Posted by Tweety
(a) Show that 3sin3θ−4cos3θ can be written in the form Rsin(3θ−α), with R>0 and 0<α<90°.

(b) Deduce the minimum value of 3sin3θ−4cos3θ and work out the smallest positive value of θ (to the nearest 0.1°) at which it occurs.

I did the first part and got $\displaystyle 5sin( 3\theta-53.1)$

but how do I find the minimum value? I have set it equal to 0, but that does not give me the correct answer.

can someone please tell me
?

Thanks!
the minimum value of 5sin(3t - 53.1) is -5 , and occurs when 3t-53.1 = 270 degrees