Math Is Fun Forum

panfilero

Member

Registered: 2010-11-27

Posts: 4

trig question

Hello,

I'm having trouble figuring out how my teacher got from this step, to this next step.

step 1:

15.5[0.866sin^2(2pi50t)+0.5(sin(2pi50t)cos(2pi50t)]

step 2:

6.71+7.75sin(2pi100t-60deg)

can anyone tell me what identities, or how the transition is made from step 1 to step 2.

much thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: trig question

Hi panfilero;

Is this what the problem reads like?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

panfilero

Member

Registered: 2010-11-27

Posts: 4

Re: trig question

Hi, yes that's it, i've been trying to plug in different identities but can't seem to get it that result

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: trig question

Hi;

Forget about plugging in identities! Try plugging in some numbers.
Ever stop to think your teacher might have made a mistake? In math a high amount of skepticism for anothers work pays off.
In other words if Newton, Gauss and 12 Archangels submitted a computation to me, I would check it! And they would certainly check my check.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

panfilero

Member

Registered: 2010-11-27

Posts: 4

Re: trig question

plugging in numbers?  Do you think there is a mistake?  This is from an old homework assignment, and it's an electronics class, there is just a little trig involved in the problem and I can't figure out the steps from getting from step 1 to step 2, the problem as a whole is larger than this, but I've been able to get this far.  I don't think there is a mistake here.

thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: trig question

Hi;

For one thing someone has done some rounding cause those 2 statements are not equal.

For the last term I use the double angle formula to get:

So we get:

That is a little closer.

Now using the following identity:

with:

Now to do the calculation:

,

The real identity is:

So he rounded 7.749... to 7.75 and -59.9992722° to = 60° to get:

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

panfilero

Member

Registered: 2010-11-27

Posts: 4

Re: trig question

Wow! I never would of got this, much thanks for your help!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: trig question

Hi panfilero;

Your welcome and welcome to the forum. He used an identity I did not know and neither did Maple or Mathematica. You can find all the moves made here at:
http://en.wikipedia.org/wiki/List_of_tr … identities

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.