<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation
Our Terms of Use (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use.

Composition of Trig Functions and Their Inverses

Application of sine, cosine, tangent, or their inverses and then another function.

Atoms Practice
Estimated15 minsto complete
Practice Composition of Trig Functions and Their Inverses
This indicates how strong in your memory this concept is
Estimated15 minsto complete
Practice Now
Turn In
Composition of Trigonometric Functions and Their Inverses

Feel free to modify and personalize this study guide by clicking "Customize".


composite function is a set of two different trigonometric functions applied to an argument in conjunction with one another.

\begin{align*}\sin(\sin^{-1}(x)) = x \cos(\cos^{-1}(x)) = x \tan(\tan^{-1}(x)) = x\end{align*}

\begin{align*}\sin^{-1}(\sin(x)) = x \cos^{-1}(\cos(x)) = x \tan^{-1}(\tan(x)) = x\end{align*}

Using the inverse of a trigonometric functions allows an argument be solved.


Trigonometry in Terms of Algebra

Remeber: All of the trig functions can be rewritten in terms of x.

License: CC BY-NC 3.0

\begin{align*}\tan \theta = \frac{x}{1}\\ \tan \theta = x hypotenuse = \sqrt{x^2+1}\\ \theta = \tan^{-1} x\end{align*}

\begin{align*}\sin (\tan^{-1}x) = \sin \theta = \frac{x}{\sqrt{x^2+1}} \csc (\tan^{-1}x) = \csc \theta = \frac{\sqrt{x^2+1}}{x}\\ \cos (\tan^{-1}x) = \cos \theta = \frac{1}{\sqrt{x^2+1}} \sec (\tan^{-1}x) = \sec \theta = \sqrt{x^2+1}\\ \tan (\tan^{-1}x) = \tan \theta = x \cot (\tan^{-1}x) = \cot \theta = \frac{1}{x}\end{align*}

Using the triangle above what type of trigonometric functions would use to solve for the triangle?

By using the Pythagoream Theorem, wou could solve for the hypotenuse of the triangle but the answer will not be a integer, instead it will be more of an expression with a variable.



Real Life Applications

Using trigonometricn functions and their inverses, you can solve real world word problem. 

Tip: Always draw a diagram after reading the word problem so that it is easier to visualize the problem and make it easier for you to solve the problem.

EX: A tower, 28.4 feet high, must be secured with a guy wire anchored 5 feet from the base of the tower. What angle will the guy wire make with the ground?

License: CC BY-NC 3.0

Explore More

Sign in to explore more, including practice questions and solutions for Applications of Inverse Trigonometric Functions.
Please wait...
Please wait...