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Evaluate sin(tan^(-1)(3/4)).
Evaluate sin(tan^(-1)(3/4)).
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Practice Questions
1 question
Q1
Evaluate sin(tan^(-1)(3/4)).
3/5
4/5
1/5
5/5
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Using the right triangle definition, sin(tan^(-1)(3/4)) = opposite/hypotenuse = 3/5.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate sin(tan^(-1)(3/4)).
Solution:
Using the right triangle definition, sin(tan^(-1)(3/4)) = opposite/hypotenuse = 3/5.
Steps: 5
Show Steps
Step 1: Understand that tan^(-1)(3/4) means we are looking for an angle whose tangent is 3/4.
Step 2: Draw a right triangle where the opposite side is 3 and the adjacent side is 4.
Step 3: Use the Pythagorean theorem to find the hypotenuse. Calculate it as: hypotenuse = sqrt(opposite^2 + adjacent^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.
Step 4: Now, find the sine of the angle. Sine is defined as opposite/hypotenuse.
Step 5: Substitute the values: sin(tan^(-1)(3/4)) = opposite/hypotenuse = 3/5.
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