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Find the value of cos(tan^(-1)(3)).
Find the value of cos(tan^(-1)(3)).
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Practice Questions
1 question
Q1
Find the value of cos(tan^(-1)(3)).
3/√10
1/√10
√10/10
1/3
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cos(tan^(-1)(3)) = 3/√10
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of cos(tan^(-1)(3)).
Solution:
cos(tan^(-1)(3)) = 3/√10
Steps: 6
Show Steps
Step 1: Understand that tan^(-1)(3) means we are looking for an angle whose tangent is 3.
Step 2: Let's call this angle θ. So, tan(θ) = 3.
Step 3: We can represent this tangent in terms of a right triangle. If the opposite side is 3 and the adjacent side is 1, we have a right triangle.
Step 4: Use the Pythagorean theorem to find the hypotenuse. The hypotenuse = √(3^2 + 1^2) = √(9 + 1) = √10.
Step 5: Now we can find cos(θ). Cosine is defined as the adjacent side over the hypotenuse. So, cos(θ) = adjacent/hypotenuse = 1/√10.
Step 6: Therefore, cos(tan^(-1)(3)) = 1/√10.
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