Table of Contents
Sum and Difference of Angles Identities
Sum of angles in a triangle is 180 degrees. Difference of angles in a triangle is also 180 degrees.
Sum and Difference Angle Formulas
The sum and difference angle formulas allow us to find the measure of an angle that is the sum or difference of two other angles.
The sum of two angles is equal to the sum of the measures of the two angles, plus the measure of the angle formed by the two angles.
The difference of two angles is equal to the difference of the measures of the two angles, minus the measure of the angle formed by the two angles.
Sum Formula for Tangent
The sum formula for tangent is a formula that calculates the tangent of a sum of two angles. The formula is written as follows:
tan(A + B) = tan(A) + tan(B)
Difference Formula for Tangent
The difference formula for tangent is a way to find the derivative of a function at a given point. The derivative of a function at a given point is the slope of the function at that point. The difference formula for tangent is:
$$\frac{d}{dx} \tan x = \frac{\tan x – \tan (x-h)}{x-h}$$
Where h is a small number.
Use of Pythagorean Theorem With the Sum and Difference Formulas
The Pythagorean theorem can be used in conjunction with the sum and difference formulas to find the length of a side of a right triangle.
The sum and difference formulas are:
a² = b² + c²
a² = b² – c²
To use the Pythagorean theorem with the sum and difference formulas, let a represent the length of the shorter side of the triangle, let b represent the length of the longer side of the triangle, and let c represent the length of the hypotenuse of the triangle.
Then, a² = b² + c² and a² = b² – c².
Since a² is the sum of b² and c², and a² is the difference of b² and c², it follows that b² = c².
Example 1:
The average person walks about 5,000 steps per day.
This is an estimate of the average number of steps a person takes in a day.
Example 2:
The following sentence: “I have a cat”
Assuming that the person has one cat, this is a true statement.
Key Takeaways
1. You can improve your writing skills by reading more.
2. You can improve your writing skills by writing more.
3. You can improve your writing skills by practicing editing and proofreading.
