Question

If P (x, y) is the point on the unit circle determined by the real number θ, then tan θ = ____

A. 1/x
B. y/x
C. x/y
D. 1/y

Please explain answer. Thank you!

Answer 1

well the unit circle looks like



so using pythagoras' theorem

you get the identity

\[x^2 + y^2 = 1\]

\[\sin(\theta) = \frac{y}{1}~~~~~~~\cos(\theta) = \frac{x}{1}\]


and lastly, using the pythagorean identity again

\[\sin^2(\theta) + \cos^2(\theta) = 1\]


hope this helps you answer the question.

Answer 2

So b. y/x?

Answer 3

that's correct

Answer 4

thank you for your help

Answer 5

and tan = sin/cos = y/x

Answer 6

hope it made sense