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What is the value of sin^(-1)(sin(π/4))?
What is the value of sin^(-1)(sin(π/4))?
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Practice Questions
1 question
Q1
What is the value of sin^(-1)(sin(π/4))?
π/4
3π/4
π/2
0
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sin^(-1)(sin(π/4)) = π/4, as π/4 is in the range of sin^(-1).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the value of sin^(-1)(sin(π/4))?
Solution:
sin^(-1)(sin(π/4)) = π/4, as π/4 is in the range of sin^(-1).
Steps: 6
Show Steps
Step 1: Understand what sin(π/4) means. π/4 is an angle in radians, which is equal to 45 degrees.
Step 2: Calculate sin(π/4). The sine of 45 degrees (or π/4 radians) is √2/2.
Step 3: Now, we need to find sin^(-1)(√2/2). This means we are looking for the angle whose sine is √2/2.
Step 4: The angle that has a sine of √2/2 is π/4 (or 45 degrees).
Step 5: Check if π/4 is within the range of the sin^(-1) function. The range of sin^(-1) is from -π/2 to π/2, and π/4 is within this range.
Step 6: Since π/4 is in the range, we can conclude that sin^(-1)(sin(π/4)) = π/4.
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