Problem 85 - Algebra and Trigonometry

Question

Use words to describe the formula for each of the following: the tangent of the difference of two angles.

Step-by-Step Solution

Answer

The tangent of the difference of two angles A and B is given by the formula \(\tan(A-B) = \frac{\tan(A) - \tan(B)}{1+\tan(A)\tan(B)}\). It represents the tangent of the angular separation between A and B.

Step 1: Explaining the concept of Tangent

The tangent of an angle in a right triangle is the ratio of the side opposite to the angle to the side adjacent to the angle. In terms of the unit circle, it is the y-coordinate divided by the x-coordinate of a point on the circle.

Step 2: Explaining the concept of Difference of Two Angles

The difference between two angles A and B is obtained by subtracting B from A. It represents the angular separation between A and B, where A > B.

Step 3: Describing the formula for the Tangent of the Difference of Two Angles

The formula for the tangent of the difference of two angles A and B is given by \(\tan(A-B) = \frac{\tan(A) - \tan(B)}{1+\tan(A)\tan(B)}\). This formula gives the tangent of the angle that is obtained by subtracting B from A.