# Sum and Difference Identity question

• May 7th 2008, 06:14 AM
masteroc
Sum and Difference Identity question
So far i have been able to do all the homework questions that i have for this, except these two.

Find the exact value for sin(x-y) under the given conditions.

sinx=24/25,0<x<pie/2; cosy=4/5,0<y<pie/2

and

sinx=2/3,pie/2<x<pie; siny=sqrt(7)/4,0<y<pie/2

Sry for writing out all the "pie's" and sqrt, but i don't know where to find the ascii equivalent.

Thanks!

P.S. Can you please explain if you skip steps or something because we just learned this and im trying to follow step by step.
• May 7th 2008, 07:10 AM
Gusbob
1) There are different ways to do question 1, but if you draw two right angle triangles for the equations you have, its very clear and can help you understand.

For example $sin\,x = \frac{24}{25} = \frac{opposite}{hypotenuse}$ -> Construct a right angle triangle and label one of the angles (Angle ABC in the diagram below) x. The opposite side of that angle will be 24 units long, and the hypotenuse is 25 units long.

http://www.themathpage.com/aTrig/Trig_IMG/7-24-25.gif
From those triangles, you could easily derive the adjacent side via Pythagoras's theorem. (25²-24²=49 = 7²)

With all the sides, you can now find the exact value of sin x, cos x, sin y, and cos y, using your basic trigonometry ratios.
Then simply use $sin (x-y) = sin\,x\,cos\,y - cos\,x\,sin\,y$

Do the same for question 2.

Because we are not considering any obtuse angles (no angle in a right angle triangle can be greater than $\frac{\pi}{2}$) , all our angles are within your limits.