1. Home
  2. >Trigonometry
  3. >Inverse Trigonometric Functions
Help

Inverse reciprocal trigonometric function: finding the exact value

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. Introduction to Inverse Reciprocal Trigonometric Function: Finding the Exact Value
?
Examples
Lessons
  1. Application of the Cancellation Laws

    Solve the following inverse trigonometric functions:

    1. sec⁡−1(sec⁡π3)\sec^{-1} (\sec \frac{\pi}{3})
    2. cot⁡(cot⁡−15)\cot (\cot^{-1} 5)
    3. csc⁡(csc⁡−112)\csc (\csc^{-1} \frac{1}{2})
  2. Solving Expressions With One Inverse Trigonometry

    Solve the following inverse trigonometric functions:

    1. csc⁡−12\csc^{-1} \sqrt 2
    2. sec⁡−113\sec^{-1} \frac{1}{3}
  3. Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry

    Solve the following inverse trigonometric functions:

    1. sec⁡(cot⁡−113)\sec (\cot^{-1} \frac{1}{\sqrt 3})
    2. cot⁡(sin⁡−113)\cot (\sin^{-1} \frac{1}{3})
    3. csc⁡(arctan⁡3x)\csc (\arctan 3x)
    4. csc⁡(cos⁡−1xx2+16)\csc (\cos^{-1} \frac{x}{\sqrt{x^{2} + 16}})
Topic Notes
?

y=csc⁡x  y = \csc x\; [−π2-\frac{\pi}{2}, 0) ∪\cup (0, π2\frac{\pi}{2}]

y=sec⁡x  y = \sec x\; [0, π2\frac{\pi}{2}) ∪\cup (π2,π\frac{\pi}{2}, \pi]

y=cot⁡x  y = \cot x\; (0, π\pi)

y=csc⁡−1x  y = \csc^{-1} x\; (-∞\infty, -1] ∪\cup [1, ∞\infty)

y=sec⁡−1x  y = \sec^{-1} x\; (-∞\infty, -1] ∪\cup [1, ∞\infty)

y=cot⁡−1x  y = \cot^{-1} x\; (-∞,∞\infty, \infty)

Basic Concepts
?