Inverse trigonometric functions review

Review your knowledge of the inverse trigonometric functions, arcsin(x), arccos(x), & arctan(x).

What are the inverse trigonometric functions?

arcsin(x)\arcsin(x), or sine, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, is the inverse of sine, left parenthesis, x, right parenthesis.
arccos(x)\arccos(x), or cosine, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, is the inverse of cosine, left parenthesis, x, right parenthesis.
arctan(x)\arctan(x), or tangent, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, is the inverse of tangent, left parenthesis, x, right parenthesis.

Range of the inverse trig functions

RadiansDegrees
π2arcsin(θ)π2-\dfrac{\pi}{2}\leq\arcsin(\theta)\leq\dfrac{\pi}{2}90arcsin(θ)90-90^\circ\leq\arcsin(\theta)\leq 90^\circ
0arccos(θ)π0\leq\arccos(\theta)\leq\pi0arccos(θ)1800^\circ\leq\arccos(\theta)\leq 180^\circ
π2<arctan(θ)<π2-\dfrac{\pi}{2}<\arctan(\theta)<\dfrac{\pi}{2}90<arctan(θ)<90-90^\circ<\arctan(\theta)<90^\circ
The trigonometric functions aren't really invertible, because they have multiple inputs that have the same output. For example, sine, left parenthesis, 0, right parenthesis, equals, sine, left parenthesis, pi, right parenthesis, equals, 0. So what should be sine, start superscript, minus, 1, end superscript, left parenthesis, 0, right parenthesis?
In order to define the inverse functions, we have to restrict the domain of the original functions to an interval where they are invertible. These domains determine the range of the inverse functions.
The value from the appropriate range that an inverse function returns is called the principal value of the function.
Want to learn more about arcsin(x)? Check out this video.
Want to learn more about arccos(x)? Check out this video.
Want to learn more about arctan(x)? Check out this video.

Check your understanding

Problem 1
The sine value of all options is 0, point, 98. Which is the principal value of arcsin(0.98)\arcsin\left(0.98\right)?
All measures are in radians.
Choose 1 answer:
Choose 1 answer:

Want to try more problems like this? Check out this exercise.