Calculating sin(A+B) using the Addition Formula for Sine

sin(A+B)

The expression sin(A+B) represents the sine of the sum of two angles, A and B

The expression sin(A+B) represents the sine of the sum of two angles, A and B. To understand how to calculate this value, we need to use a trigonometric identity, specifically the addition formula for sine.

The addition formula for sine states that sin(A+B) equals sin(A)cos(B) + cos(A)sin(B).

This formula tells us that to find the value of sin(A+B), we need to know the values of sin(A), sin(B), cos(A), and cos(B).

Let’s break down the steps to find sin(A+B) using this formula:

Step 1: Determine the values of sin(A), sin(B), cos(A), and cos(B):
– sin(A) can be found by using the sine function with angle A.
– sin(B) can be found by using the sine function with angle B.
– cos(A) can be found by using the cosine function with angle A.
– cos(B) can be found by using the cosine function with angle B.

Step 2: Substitute the values of sin(A), sin(B), cos(A), and cos(B) into the addition formula:

sin(A+B) = sin(A)cos(B) + cos(A)sin(B)

Step 3: Calculate the multiplications in the formula:
– Multiply sin(A) with cos(B).
– Multiply cos(A) with sin(B).

These multiplications should give you two values.

Step 4: Add the two values from Step 3:
– Add the value of sin(A)cos(B) with the value of cos(A)sin(B).

The result of this addition will be the value of sin(A+B).

Keep in mind that when dealing with angles, it is important to use the correct unit of measurement (radians or degrees) as required by the problem or context.

I hope this detailed explanation helps you understand how to calculate sin(A+B) using the addition formula for sine. If you have any further questions or need additional clarification, please feel free to ask.

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