Problem 86
Question
Use words to describe the formula for each of the following: the tangent of the sum of two angles.
Step-by-Step Solution
Verified Answer
The formula for the tangent of the sum of two angles is \[\tan(\alpha + \beta) = \frac {\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}\]
1Step 1: Explanation of Tangent
Tangent is a basic function in trigonometry. It is the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
2Step 2: Introduction of Angle Sum
The sum of two angles \(\alpha\) and \(\beta\) will be denoted as \(\alpha + \beta\). The tangent of this sum can be expressed in terms of the tangents of \(\alpha\) and \(\beta\) itself.
3Step 3: Tangent Sum Formula
The formula for the tangent of the sum of two angles is written as: \[\tan(\alpha + \beta) = \frac {\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}\] This formula is derived from the sine and cosine angle sum identities.
Other exercises in this chapter
Problem 85
Use a calculator to solve each equation, correct to four decimal places, on the interval \([0,2 \pi)\) $$ \sin x=0.8246 $$
View solution Problem 85
Use words to describe the formula for: the power-reducing formula for the sine squared of an angle.
View solution Problem 86
Use a calculator to solve each equation, correct to four decimal places, on the interval \([0,2 \pi)\) $$ \sin x=0.7392 $$
View solution Problem 86
Use words to describe the formula for: the power-reducing formula for the cosine squared of an angle.
View solution