Math Problem Statement

sin^(-1)1

Solution

The expression sin1(1)\sin^{-1}(1) refers to the inverse sine (or arcsine) of 1.

In trigonometry, sin1(x)\sin^{-1}(x) gives the angle whose sine is xx. So, we are looking for the angle θ\theta such that:

sin(θ)=1\sin(\theta) = 1

The sine of θ=π2\theta = \frac{\pi}{2} (or 90°) is 1. Therefore:

sin1(1)=π2\sin^{-1}(1) = \frac{\pi}{2}

Thus, the answer is:

π2\boxed{\frac{\pi}{2}}

Would you like more details or have any further questions?

Here are five related questions to explore further:

  1. What is sin1(0)\sin^{-1}(0)?
  2. How do you compute the inverse sine of negative numbers?
  3. What is the range of the inverse sine function?
  4. Can you explain how the sine and inverse sine functions are related graphically?
  5. How do you calculate inverse trigonometric functions using a calculator?

Tip: Remember that the range of sin1(x)\sin^{-1}(x) (arcsine) is restricted to [π2,π2][-\frac{\pi}{2}, \frac{\pi}{2}].

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Inverse Trigonometric Functions

Formulas

sin^(-1)(x)
sin(θ) = 1

Theorems

Arcsine Function
Range of Inverse Sine Function

Suitable Grade Level

Grades 10-12