For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is equivalent to tan A? a. x/y b. y/x c. x/√x^2+y^2 d. y/√x^2+y^2

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Mathematics

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16 October, 19:05

For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is equivalent to tan A? a. x/y b. y/x c. x/√x^2+y^2 d. y/√x^2+y^2

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Answers (1)

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Evan Pollard · Answer 1

Draw a right triangle ABC so that m∠C = 90°

The lengths are:

Side a is opposite ∠A,

Side b is opposite ∠B,

Side c (the hypotenuse) is opposite ∠C

Because cos A = x, therefore

x = b/c = > b = cx (1)

Because sin A = y, therefore

y = a/c = > a = cy (2)

By definition,

tan A = a/b

= (cy) / (cx)

= y/x

Answer: b. y/x