Question

The point (2, 3) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ?

Answer 1

Answer:

sin Ф = 3/√13; cos Ф = 2/√13; and tan Ф = 3/2

Step-by-step explanation:

Let's assume we're limiting ourselves to Quadrant I.

Start with the tangent function.  tan Ф = opp / adj.

In this case opp = 3 and adj = 2.  

The length of the hypotenuse is found using the Pythagorean Theorem and is √(3² + 2²) = √13.

Then sin Ф = opp / hyp = 3/√13 or 3√13/13

and

cos Ф = adj / hyp = 2/√13 or 2√13/13

and (as before)

tan Ф =  opp / adj = 3/2