Compound Angle Formula for Trig Functions

In summary, the conversation is about a question that requires using an appropriate compound angle formula to simplify an expression involving trigonometric functions. The person has solved for one side of the equation but is having trouble relating one of the angles to a special triangle. They are looking for help in understanding how to solve for the missing parts of the equation.
  • #1
zycismia
1
0

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
 
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  • #2
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)
 
  • #3
zycismia said:

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 .
 

1. What is the compound angle formula and how is it used?

The compound angle formula is used in trigonometry to find the sine, cosine, and tangent of a sum or difference of two angles. It is given by:sin(A ± B) = sinAcosB ± cosAsinBcos(A ± B) = cosAcosB ∓ sinAsinBtan(A ± B) = (tanA ± tanB) / (1 ∓ tanAtanB)This formula is useful in solving problems involving multiple angles, such as finding the height of a building using the angle of elevation and the distance from the base.

2. How do I determine which sign to use in the compound angle formula?

The sign to use in the compound angle formula depends on the quadrant in which the angles A and B lie. If both angles are in the same quadrant, then the same sign is used in the formula. If they are in different quadrants, then the sign is determined by the following rules:- If A is in the first quadrant and B is in the second quadrant, use the positive sign in the formula.- If A is in the second quadrant and B is in the first quadrant, use the negative sign in the formula.- If A is in the third quadrant and B is in the fourth quadrant, use the positive sign in the formula.- If A is in the fourth quadrant and B is in the third quadrant, use the negative sign in the formula.

3. Can the compound angle formula be used for any type of triangle?

No, the compound angle formula is only applicable for right triangles. It involves the trigonometric functions sine, cosine, and tangent, which are defined for right triangles only.

4. Is there a specific order in which the angles must be written in the compound angle formula?

Yes, the angles must be written in a specific order for the formula to give the correct result. The first angle, A, should always be the larger angle, and the second angle, B, should be the smaller angle. This order is important because the formula involves adding or subtracting the angles.

5. How can I use the compound angle formula to solve real-life problems?

The compound angle formula can be used to solve a variety of real-life problems involving angles and distances, such as finding the height of a building, the distance between two points, or the angle of elevation for a ladder. By using this formula, you can calculate the trigonometric functions of a sum or difference of angles, which can then be used to solve these types of problems.

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