1. ## Trigonometry...test tomorrow!

Hello everyone so I have a math test tomorrow and im stuck on a review question. It's trigonometry in a functions class. I was just wondering if anyone would be able to figure it out.

heres the question

1. Given sinx + cosx = 2/3 , calculate the value of sin2x

any help will be appreciated.

2. Originally Posted by aries
Hello everyone so I have a math test tomorrow and im stuck on a review question. It's trigonometry in a functions class. I was just wondering if anyone would be able to figure it out.

heres the question

1. Given sinx + cosx = 2/3 , calculate the value of sin2x

any help will be appreciated.
$\sin x + \cos x = \frac 23$

$\Rightarrow (\sin x + \cos x)^2 = \frac 49$

$\Rightarrow \sin^2 x + 2 \sin x \cos x + \cos^2 x = \frac 49$

can you continue?

3. I understand how you got to the 3rd step however i still don't know what to do after that. Do I factor it? or is there an identity that I need to use to continue?

-thanks

4. The double angle formula states that sin2x = 2*sinx*cosx. That may be helpful along with another trig identity. I suggest memorizing these. If its anything like my highschool trig classes, you will be using them a lot. Many problems can be solved by using a well defined procedure for that given class of problems, combined with a trick. Many students know the procedure but have trouble finding the trick. In this case, I would consider the identities the trick.

5. Originally Posted by sixstringartist
The double angle formula states that sin2x = 2*sinx*cosx. That may be helpful along with another trig identity. I suggest memorizing these. If its anything like my highschool trig classes, you will be using them a lot. Many problems can be solved by using a well defined procedure for that given class of problems, combined with a trick. Many students know the procedure but have trouble finding the trick. In this case, I would consider the identities the trick.
right you are.

@ aries: the other identity you MUST know is $\sin^2 x + \cos^2 x = 1$

now can you continue?

6. great! I'm pretty sure I can finish it now.
thanks for the help. to both of you.