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Find the value of sin^(-1)(sin(π/4)).
Find the value of sin^(-1)(sin(π/4)).
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Practice Questions
1 question
Q1
Find the value of sin^(-1)(sin(π/4)).
π/4
3π/4
π/2
0
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Since sin(π/4) = 1/√2, sin^(-1)(1/√2) = π/4.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of sin^(-1)(sin(π/4)).
Solution:
Since sin(π/4) = 1/√2, sin^(-1)(1/√2) = π/4.
Steps: 6
Show Steps
Step 1: Understand that sin^(-1) is the inverse function of sin. It gives us the angle whose sine is a given value.
Step 2: Calculate sin(π/4). We know that π/4 radians is equal to 45 degrees.
Step 3: Find the sine of 45 degrees (or π/4 radians). The value is 1/√2.
Step 4: Now we need to find sin^(-1)(1/√2). This means we are looking for the angle whose sine is 1/√2.
Step 5: The angle that has a sine of 1/√2 is π/4 (or 45 degrees).
Step 6: Therefore, sin^(-1)(sin(π/4)) = sin^(-1)(1/√2) = π/4.
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