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If x = cos^(-1)(1/2), then the value of sin(x) is:
If x = cos^(-1)(1/2), then the value of sin(x) is:
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Practice Questions
1 question
Q1
If x = cos^(-1)(1/2), then the value of sin(x) is:
1/2
√3/2
1
0
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If x = cos^(-1)(1/2), then x = π/3. Therefore, sin(x) = sin(π/3) = √3/2.
Questions & Step-by-step Solutions
1 item
Q
Q: If x = cos^(-1)(1/2), then the value of sin(x) is:
Solution:
If x = cos^(-1)(1/2), then x = π/3. Therefore, sin(x) = sin(π/3) = √3/2.
Steps: 5
Show Steps
Step 1: Understand that cos^(-1)(1/2) means we are looking for an angle x whose cosine value is 1/2.
Step 2: Recall the unit circle or the values of cosine for common angles. The angle x that has a cosine of 1/2 is π/3 (or 60 degrees).
Step 3: Now that we have x = π/3, we need to find sin(x).
Step 4: Use the known value of sin(π/3). From trigonometric values, sin(π/3) = √3/2.
Step 5: Therefore, the value of sin(x) is √3/2.
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