Using Trigonometric Identity: Finding the Value of sin(A-B) in Radians

sin(A-. b)

To find the value of `sin(A-B)`, we can use the trigonometric identity for the sine of a difference of angles:

sin(A-B) = sin(A)cos(B) – cos(A)sin(B)

Here we assume that `A` and `B` are angles measured in radians

To find the value of `sin(A-B)`, we can use the trigonometric identity for the sine of a difference of angles:

sin(A-B) = sin(A)cos(B) – cos(A)sin(B)

Here we assume that `A` and `B` are angles measured in radians.

This identity can be derived from the trigonometric sum formulas:

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

By manipulating the sum formula, we can obtain the difference formula for sine.

Let’s go through an example.

Example:
Suppose we have A = π/3 and B = π/6 (both measured in radians). We want to find sin(π/3 – π/6).

Using the formula, we have:
sin(A-B) = sin(π/3)cos(π/6) – cos(π/3)sin(π/6)

Since sin(π/3) = sqrt(3)/2 and cos(π/6) = sqrt(3)/2, and cos(π/3) = 1/2 and sin(π/6) = 1/2, we can substitute these values in:

sin(A-B) = (sqrt(3)/2)(sqrt(3)/2) – (1/2)(1/2)
= 3/4 – 1/4
= 2/4
= 1/2

Therefore, sin(π/3 – π/6) = 1/2.

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