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If x = tan^(-1)(√3), what is the value of sin(2x)?
If x = tan^(-1)(√3), what is the value of sin(2x)?
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Practice Questions
1 question
Q1
If x = tan^(-1)(√3), what is the value of sin(2x)?
√3/2
1
√2/2
0
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Since tan^(-1)(√3) = π/3, then 2x = 2π/3 and sin(2x) = sin(2π/3) = √3/2.
Questions & Step-by-step Solutions
1 item
Q
Q: If x = tan^(-1)(√3), what is the value of sin(2x)?
Solution:
Since tan^(-1)(√3) = π/3, then 2x = 2π/3 and sin(2x) = sin(2π/3) = √3/2.
Steps: 8
Show Steps
Step 1: Understand that x = tan^(-1)(√3) means we are looking for an angle whose tangent is √3.
Step 2: Recall that tan(π/3) = √3. Therefore, x = π/3.
Step 3: Calculate 2x by multiplying x by 2: 2x = 2 * (π/3) = 2π/3.
Step 4: Now, we need to find sin(2x), which is sin(2π/3).
Step 5: Recognize that sin(2π/3) is the same as sin(π - π/3).
Step 6: Use the sine identity: sin(π - θ) = sin(θ). So, sin(2π/3) = sin(π/3).
Step 7: Recall that sin(π/3) = √3/2.
Step 8: Therefore, sin(2x) = √3/2.
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