# Thread: Trig Identities (Sum and double Angle)

1. ## Trig Identities (Sum and double Angle)

Hi guys, i have a couple question from my homework i am having trouble with a little more then a couple , if any one could help i would appreciate it.

1) Simplify or combine where possible, sin(x + x) = i get 2sinx (Answer is sin2x) why is the 2 there? not in front?
2)
5sinxsinx = i get 5sinx^2 (answer is 5sin^2x)

2. ## Re: Trig Identities (Sum and double Angle)

Surely you understand that x + x = 2x...

As for the second, if you meant $$\displaystyle 5\left[ \sin{(x)} \right] ^2$$, this is an equivalent way of writing $\displaystyle 5\sin^2{(x)}$ so you would be correct. However, if you meant $\displaystyle 5\sin{ \left( x^2 \right) }$ you would be wrong.

3. ## Re: Trig Identities (Sum and double Angle)

1+1 = 2 O.O who would of guessed yeah i get that lol.

For the second one it is not showing your text correctly. My answer is 5sinx(sinx)= 5

Thanks for the help.

4. ## Re: Trig Identities (Sum and double Angle)

What? You think that sinx(sinx)= 1? For any a, a times a is designated " $a^2$". That's what that " $^2$" means. So in particular, $(sin x)(sin x)= (sin x)^2$ and $sin^2 x$ is just simpler notation. Strictly speaking "x" is an argument of the function "sin" so we should have parentheses. Perhaps if it were (sin(x))(sin(x)) it would be clearer that it should be sin^2(x), not " $sin x^2$" which would be interpreted as " $sin(x^2)$".

5. ## Re: Trig Identities (Sum and double Angle)

After reading your comments i understand what i was not getting sometimes its the simple things that get me, One last follow up question if you math wizards don't mind,

Prove the following Cos(x-Pi)=Sin(x+3pi/2) : What i attempted to do was use the identity Sin(a+b)= sinAcosB+cosAsinB it came close but not what i needed, would any one be able to help?.

Thanks for all the help again i really do love this site, and sorry for my stupid questions .

6. ## Re: Trig Identities (Sum and double Angle)

Expand both sides of the equation using the cosine and sine angle addition identity, respectively.

7. ## Re: Trig Identities (Sum and double Angle)

Thanks that worked.