Need methodology help concerning multiplication of trig func

[MAC-A-TAC]

When multiplying say for example (12 sin 2t)(12 sin 5t), how do you handle the 2t and 5t? :?
Thank you for your help.

 

[wjm11]

When multiplying say for example (12 sin 2t)(12 sin 5t), how do you handle the 2t and 5t?

(sint 2t)*(sin 5t) does not equal (sin 10t^2), if that’s is what you were wondering. You would need to break them down first using sum and difference formulas and/or double angle formulas, in order to get them both in terms of sin x, for example. Then you would be able to further simplify/combine terms.

 

[MAC-A-TAC]

Thanks for the response.
Alright, 12 sin 2t would be 12(2sin t cos t) or 24sin t cos t. How would I handle the second term 12 sin 5t?

Much obliged...again.

 

[wjm11]

How would I handle the second term 12 sin 5t?

Sin 5t can be rewritten as sin (3t + 2t), right?

Now use the “sum” formula: sin (A + B) = sinAsinB + cosAcosB.

From there, use the “double angle” (which you’ve already shown) and the “triple angle” formulas to further simplify. One good source of info for these formulas is at wikipedia:

http://en.wikipedia.org/wiki/List_of_tr ... identities

Many sources are available.

Hope that helps.

 

[MAC-A-TAC]

Yes that is very helpful.

Thank you.