sin(A+. b)
To find the value of sin(A+B), we will use a trigonometric identity known as the sum formula for sine:
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
This formula allows us to express the sine of the sum of two angles in terms of the sines and cosines of the individual angles
To find the value of sin(A+B), we will use a trigonometric identity known as the sum formula for sine:
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
This formula allows us to express the sine of the sum of two angles in terms of the sines and cosines of the individual angles.
Let’s break down the formula step by step:
1. Start with sin(A+B)
2. Rewrite sin(A)cos(B) + cos(A)sin(B)
3. Substitute the values of sin(A) and sin(B) using their respective angle measures
4. Substitute the values of cos(A) and cos(B) using their respective angle measures
5. Calculate the products of sin(A)cos(B) and cos(A)sin(B)
6. Add the calculated values of sin(A)cos(B) and cos(A)sin(B)
For example, let’s calculate sin(30° + 45°):
1. sin(30° + 45°)
2. sin(30°)cos(45°) + cos(30°)sin(45°)
3. (1/2)(√2/2) + (√3/2)(√2/2)
4. (√2/4) + (√6/4)
5. Multiply (√2/4) by 1 and (√6/4) by 1 to simplify the expression
6. (√2 + √6)/4
Therefore, sin(30° + 45°) = (√2 + √6)/4
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