Trigonometric inverse functions

In summary, trigonometric inverse functions are mathematical functions that provide the inverse relationship to the standard trigonometric functions. Their main purpose is to find the angle measure of a right triangle and they are represented in mathematical notation by adding a prefix to the standard trigonometric function. The domain of these functions is limited and the range is typically in radians. They can be evaluated using a calculator, trigonometric identities, or the unit circle.
  • #1
lizzie
25
0
i want the most general solution for
sin6x=sin4x-sin2x
 
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  • #2
sin6x=sin4x-sin2x

sin6x-sin4x+sin2x=0

Then remember that

[tex]sinP+sinQ=2sin(\frac{P+Q}{2})cos(\frac{P-Q}{2})[/tex]
 
  • #3
thanks
 

FAQ: Trigonometric inverse functions

1. What are trigonometric inverse functions?

Trigonometric inverse functions are mathematical functions that provide the inverse relationship to the standard trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant). They are also known as arc functions or anti-trigonometric functions.

2. What is the purpose of using trigonometric inverse functions?

The main purpose of using trigonometric inverse functions is to find the angle measure of a right triangle when given the ratio of its sides. They are also used to solve trigonometric equations and to simplify complex trigonometric expressions.

3. How are trigonometric inverse functions represented in mathematical notation?

Trigonometric inverse functions are typically denoted by adding the prefix "arc" or "a" in front of the standard trigonometric function. For example, the inverse of sine is written as "arcsin" or "asin", and the inverse of cosine is written as "arccos" or "acos".

4. What is the domain and range of trigonometric inverse functions?

The domain of trigonometric inverse functions is limited to specific intervals depending on the trigonometric function being inverted. Generally, the domain includes values between -1 and 1. The range of trigonometric inverse functions is typically in radians, but can also be in degrees.

5. How are trigonometric inverse functions evaluated?

Trigonometric inverse functions are evaluated using a calculator or by using trigonometric identities and special triangles. They can also be evaluated using the unit circle, where the coordinates on the circle correspond to the trigonometric ratios of the angle.

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