# Thread: Solving using sin(A+B) and cos rule

1. ## Solving using sin(A+B) and cos rule

I need someone to solve this for me. I don't understand it so i'm hoping once i see how it solved i will be able to do the rest. Thanks a mill.

1) Using the identities for sin(A+B) and cos^2(theta)+sin^2(theta)=1.

Find sine 65 degrees, given that sin 40(degrees)=0.643 and sin 25(degrees)=0.423?

2. You should know that

$\displaystyle \sin{(A+B)} = \sin{A}\cos{B} + \cos{A}\sin{B}$.

So $\displaystyle \sin{65^{\circ}} = \sin{40^{\circ}}\cos{25^{\circ}} + \cos{40^{\circ}}\sin{25^{\circ}}$.

Use the Pythagorean Identity to find $\displaystyle \cos{25^{\circ}}$ and $\displaystyle \cos{40^{\circ}}$...

3. Thankyou so much. So do i now substitute the values in to replace the sin and cos.

So (0.643 + 0.423) + (0.423 + ).643)

???

4. You would if you had the correct values for $\displaystyle \cos{25^{\circ}}$ and $\displaystyle \cos{40^{\circ}}$...

Like I said, you have to use the Pythagorean Identity to find these values. Then you can substitute your 4 values into the sum rule.

5. Why on earth did you post this question for the third time?

http://www.mathhelpforum.com/math-he...em-153105.html

http://www.mathhelpforum.com/math-he...em-153216.html

Are people not allowed to bump their own threads or something!?!?