Evaluate the expression. sin − 1 1 \sin^{-1}1 sin − 1 1

In this problem, we're asked to evaluate the expression at the inverse sine of 1. Remember, we can think of this as, okay, the sine of what angle is equal to 1, and we're trying to find what angle makes that true. Now looking at my unit circle, I know my value has to be in between negative pi over 2 and positive pi over 2. And because I'm taking the inverse sine of a positive value, I know that my answer has to be in quadrant 1 where all of my sine values are positive. Now I also know that the sine of pi over 2 is 1 because this is one of my quadrantal angles. So this is my solution here, pi over 2, because the sine of pi over 2 is equal to 1. Now my solution is done and we are good to go. Thanks for watching and let me know if you have questions.

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0. Functions7h 52m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation3h 18m
4. Applications of Derivatives2h 38m
5. Graphical Applications of Derivatives6h 2m
6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
7. Antiderivatives & Indefinite Integrals1h 26m
8. Definite Integrals4h 44m
9. Graphical Applications of Integrals2h 27m
- Area Between Curves
  1h 18m
- Introduction to Volume & Disk Method
  1h 8m
10. Physics Applications of Integrals 3h 16m
- Kinematics
  1h 13m
- Work
  2h 3m
11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
12. Techniques of Integration7h 39m
13. Intro to Differential Equations2h 55m
14. Sequences & Series5h 36m
15. Power Series2h 19m
- Introduction to Power Series
  1h 9m
- Taylor Series & Taylor Polynomials
  1h 10m
16. Parametric Equations & Polar Coordinates7h 58m

0. Functions

Inverse Trigonometric Functions

Calculus

0. Functions

Inverse Trigonometric Functions

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Multiple Choice

Evaluate the expression.
$\sin^{-1}1$

$0$

$pi over 2$

$π$

$- \frac{π}{2}$

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Verified step by step guidance

Understand that $ \sin^{-1}(x) $ represents the inverse sine function, also known as arcsin, which gives the angle whose sine is $ x $.

Recognize that the expression $ \sin^{-1}(1) $ asks for the angle whose sine is 1.

Recall that the sine of $ \frac{\pi}{2} $ is 1, which means $ \sin(\frac{\pi}{2}) = 1 $.

Therefore, $ \sin^{-1}(1) = \frac{\pi}{2} $ because $ \frac{\pi}{2} $ is the angle in the range $[-\frac{\pi}{2}, \frac{\pi}{2}]$ that satisfies this condition.

Conclude that the value of the expression $ \sin^{-1}(1) $ is $ \frac{\pi}{2} $.