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Find the value of sin(cos^(-1)(1/2)).
Find the value of sin(cos^(-1)(1/2)).
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Practice Questions
1 question
Q1
Find the value of sin(cos^(-1)(1/2)).
√3/2
1/2
0
1
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Let θ = cos^(-1)(1/2). Then cos(θ) = 1/2, which corresponds to θ = π/3. Therefore, sin(θ) = sin(π/3) = √3/2.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of sin(cos^(-1)(1/2)).
Solution:
Let θ = cos^(-1)(1/2). Then cos(θ) = 1/2, which corresponds to θ = π/3. Therefore, sin(θ) = sin(π/3) = √3/2.
Steps: 5
Show Steps
Step 1: Understand that cos^(-1)(1/2) means we are looking for an angle θ such that the cosine of θ equals 1/2.
Step 2: Recall that cos(π/3) = 1/2. Therefore, we can say θ = π/3.
Step 3: Now, we need to find sin(θ). Since we found θ = π/3, we will calculate sin(π/3).
Step 4: Recall the value of sin(π/3). It is known that sin(π/3) = √3/2.
Step 5: Therefore, the value of sin(cos^(-1)(1/2)) is √3/2.
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