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What is the value of sin(tan^(-1)(1))?
What is the value of sin(tan^(-1)(1))?
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Practice Questions
1 question
Q1
What is the value of sin(tan^(-1)(1))?
1/√2
1/2
1
√2/2
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sin(tan^(-1)(1)) = √2/2
Questions & Step-by-step Solutions
1 item
Q
Q: What is the value of sin(tan^(-1)(1))?
Solution:
sin(tan^(-1)(1)) = √2/2
Steps: 6
Show Steps
Step 1: Understand that tan^(-1)(1) means we are looking for an angle whose tangent is 1.
Step 2: Recall that the tangent of 45 degrees (or π/4 radians) is 1.
Step 3: Therefore, tan^(-1)(1) = 45 degrees (or π/4 radians).
Step 4: Now, we need to find the sine of 45 degrees (or π/4 radians).
Step 5: The sine of 45 degrees is known to be √2/2.
Step 6: Thus, sin(tan^(-1)(1)) = sin(45 degrees) = √2/2.
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