Compound Angle Formula for Trig Functions

[zycismia]

Homework Statement

hello i am having trouble with a question here it is

use an appropriate compound angle formula to express a a single trig formula than determine an exact formula for each

a) sin pi/4 cos pi/12 +cos pi/4 sin pi/12

so i got most of it i put it into the fourmla sin(x+y)=sinxcosx+cosysinx

i solved for the right side and got square root of 3 over 2
but for the left side i am having trouble relating pi/12 to a special triangle as it is only 15
so far i am only able to do
sin pi/4 cos pi/12 + cos pi/4 sin pi/12
1/sq root of2 + blank+1/sq of root 2 + blank

as you can see i can solve the cos pi/12 and sin pi/12 if some one could please help me and show full steps as there is the same numbers for the diff compound formulas so i can see how to solve those
thank you

 

[AJ Bentley]

I have no idea what you are doing!
The question looks like you have to use sin(A + B) to simplify the expression given.

In which case it's just sin(pi/4 + pi/12).
which is sin(pi/3)

 

[SammyS]

Homework Statement

hello i am having trouble with a question here it is

use an appropriate compound angle formula to express a a single trig formula then determine an exact formula for each

a) sin pi/4 cos pi/12 +cos pi/4 sin pi/12

so i got most of it i put it into the formula sin(x+y)=sinxcosx+cosysinx

i solved for the right side and got square root of 3 over 2
but for the left side i am having trouble relating pi/12 to a special triangle as it is only 15
so far i am only able to do
sin pi/4 cos pi/12 + cos pi/4 sin pi/12
1/sq root of2 + blank+1/sq of root 2 + blank

as you can see i can solve the cos pi/12 and sin pi/12 if some one could please help me and show full steps as there is the same numbers for the diff compound formulas so i can see how to solve those
thank you

Hello zycismia. Welcome to PF !

That should be: (1/(sq root of 2)) (times) blank1 + (1/(sq of root 2)) (times) blank2 .