Math Problem Statement
Question content area top Part 1 Find the exact value of the following expression. sine Superscript negative 1 Baseline left parenthesis StartFraction StartRoot 2 EndRoot Over 2 EndFraction right parenthesis Question content area bottom Part 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sine Superscript negative 1 Baseline left parenthesis StartFraction StartRoot 2 EndRoot Over 2 EndFraction right parenthesis equals
enter your response here (Simplify your answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression.) B. The function is not defined.
Solution
The given expression is:
The value of gives the angle such that and is in the range .
For , the angle whose sine is is (or ).
Thus, the exact value is:
Final Answer: A.
Would you like more explanation on this? Here are 5 follow-up questions:
- What is the domain and range of ?
- Why does satisfy the inverse sine definition?
- How can this concept be extended to other inverse trigonometric functions?
- What happens if the value of is outside its defined range?
- How is related to arcsine?
Tip: Memorizing key sine, cosine, and tangent values for angles like will speed up solving problems like this!
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Math Problem Analysis
Mathematical Concepts
Inverse Trigonometric Functions
Sine Function
Unit Circle
Formulas
sin⁻¹(x) gives θ such that sin(θ) = x, where θ ∈ [-π/2, π/2]
Theorems
Definition of Inverse Sine Function
Key Trigonometric Values
Suitable Grade Level
Grades 10-12