A Step-by-Step Guide to Evaluating sin(A-B) Using Trigonometric Identity

sin(A-B)

To find the value of sin(A-B), we can use the trigonometric identity:

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

This identity allows us to express the sine of the difference of two angles, A and B, in terms of the sines and cosines of those two angles separately

To find the value of sin(A-B), we can use the trigonometric identity:

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

This identity allows us to express the sine of the difference of two angles, A and B, in terms of the sines and cosines of those two angles separately.

Let’s break down the steps to evaluate sin(A-B):

Step 1: Determine the values of sin(A) and cos(A)
To find the value of sin(A), you need to know the angle A. Look up the sine value corresponding to that angle on a table or use a calculator. Similarly, find the value of cos(A) for the angle A.

Step 2: Determine the values of sin(B) and cos(B)
In the same manner as in step 1, find the values of sin(B) and cos(B) for the angle B.

Step 3: Substitute the values into the formula
Plug the values of sin(A), sin(B), cos(A), and cos(B) into the formula:

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

Replace sin(A) with the value obtained in step 1, and cos(A) with the corresponding value. Also, substitute sin(B) and cos(B) with the values obtained in step 2.

Step 4: Calculate
Evaluate the formula using the substituted values and perform the necessary arithmetic operations to find the final answer for sin(A-B).

Remember to consider the units of measurement (radians or degrees) for the angles A and B, and ensure that the calculator or table being used is appropriate for the unit being used.

In summary, to find the value of sin(A-B), you need to know the values of sin(A), cos(A), sin(B), and cos(B), which can be obtained from a table or calculator. Substitute these values into the formula sin(A-B) = sin(A)cos(B) – cos(A)sin(B) and perform the calculations to get the final answer.

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