Question

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

Answer 1

y/x or y over x

Explanation:

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?

Odyssey question

Answer 2

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