Trigonometric sum-difference formula for absolute values

Thread starter xooberon
Start date Mar 9, 2010
Tags

Absolute Absolute values Formula Trigonometric

In summary, the Trigonometric sum-difference formula for absolute values is a useful tool for simplifying complex trigonometric expressions and solving equations involving absolute values. However, it can only be used when the trigonometric functions have the same argument and coefficient, and the same sign on the absolute value. It is also related to the Pythagorean identity, and can be used for all trigonometric functions with the same restrictions.

Mar 9, 2010

xooberon

sin|x + y| = ?
cos|x + y| = ?

Is there any formula for these?

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Mar 9, 2010

CRGreathouse

Science Advisor

Homework Helper

You can use the even/oddness of the functions to remove the abs bars or shift it to a constant outside, then apply the normal sum-difference formulas.

1. What is the Trigonometric sum-difference formula for absolute values?

The Trigonometric sum-difference formula for absolute values is a formula used to simplify the sum or difference of two trigonometric functions with absolute values. It is expressed as:

|sin(x) ± sin(y)| = 2|sin((x ± y)/2) * cos((x ± y)/2)|

2. When is the Trigonometric sum-difference formula for absolute values most useful?

This formula is most useful when trying to simplify complex trigonometric expressions involving absolute values. It can also be used to solve trigonometric equations involving absolute values.

3. Are there any restrictions when using the Trigonometric sum-difference formula for absolute values?

Yes, there are some restrictions when using this formula. Both trigonometric functions must have the same argument, and the argument must be in the form of x ± y. Additionally, both functions must have the same coefficient and the same sign on the absolute value.

4. How does the Trigonometric sum-difference formula for absolute values relate to the Pythagorean identity?

The Pythagorean identity (sin²(x) + cos²(x) = 1) is a special case of the Trigonometric sum-difference formula for absolute values. When x and y are the same value, the formula simplifies to sin²(x) + cos²(x) = 2|sin(x)| * cos(x), which is equivalent to the Pythagorean identity.

5. Can the Trigonometric sum-difference formula for absolute values be used for all trigonometric functions?

Yes, this formula can be used for all trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant. However, the restrictions mentioned in question 3 still apply.