Cosine Identities. Find the exact value of cos(x+y), given 0

Question

Cosine Identities. Find the exact value of cos(x+y), given 0 <x< pi ; 0 <y <pi.

cos(x) = 4/5 ; cos(y) = 12/13

campbell_st · Answer

You have 2 different triangles, 1st one contains angle x and has an adjacent side of 4 and hypotenuse of 5. The 2nd triangle has an adjacent side of 12 and hypotenuse of 13.

In both triangles you need to find the opposite side using pythagoras'theorem. Then you can find sin(x) and sin(y).

When you have the sin ratios you can then use

Cos(x+y) = cos(x)cos(y) -sin(x)sin(y)

Substitute the exact values forr each ratio to get the answer.

Hope it helps

campbell_st · Answer

Both the angles x and y are 1st quadrant angles since the ratios are positive and the restricted domains

blackbird02 · Answer

so, the opposite side in the first is 3 and on the second its 5, is this correct? @campbell_st

anonymous · Answer

@blackbird02 yes your right now find the sin(x) and sin(y)

blackbird02 · Answer

@Sambhavvinaykya  I'm not sure what sin(x) and sin(y) should be. Is it 4/5 and 2/5 ?

anonymous · Answer

first draw the two triangles
|dw:1420459461135:dw|

anonymous · Answer

now find sin(x)=opp/hyp
and find sin(y)

anonymous · Answer

your sin(x)=4/5 u were correct but sin(y) is wrong

blackbird02 · Answer

oh, sorry. i meant 5/13 ? I've already solved the exact value. It's 28/65.

anonymous · Answer

how come |dw:1420460791116:dw|