# Trig Identities (Sum and double Angle)

• April 2nd 2013, 03:10 PM
Gurp925
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)

• April 2nd 2013, 03:25 PM
Prove It
Re: Trig Identities (Sum and double Angle)
Surely you understand that x + x = 2x...

As for the second, if you meant [tex]\displaystyle 5\left[ \sin{(x)} \right] ^2 [/math], 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.
• April 2nd 2013, 04:30 PM
Gurp925
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.
• April 2nd 2013, 04:44 PM
HallsofIvy
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 " $sin(x^2)$".
• April 3rd 2013, 10:43 PM
Gurp925
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 :(.
• April 3rd 2013, 11:20 PM
SworD
Re: Trig Identities (Sum and double Angle)
Expand both sides of the equation using the cosine and sine angle addition identity, respectively.
• April 3rd 2013, 11:55 PM
Gurp925
Re: Trig Identities (Sum and double Angle)
Thanks that worked.