Question

(10.02)

The point (2,3) is on the terminal side of angle in standard

position. What are the values of sine, cosine, and tangent of O?

Make sure to show all work. (10 points)

Answer 1

Answer:

$sin O=\dfrac{3\sqrt{13}}{13}\\cos O=\dfrac{2\sqrt{13}}{13}\\tan O=\dfrac{3}{2}$

Step-by-step explanation:

If the point (2,3) is on the terminal side of an angle in standard position.

Adjacent of O, x=2,

Opposite of O, y=3

Next, we determine the hypotenuse, r using Pythagoras Theorem.

$Hypotenuse =\sqrt{Opposite^2+Adjacent^2} \\r=\sqrt{3^2+2^2} \\r=\sqrt{13}$

Therefore:

$sin O=\dfrac{Opposite}{Hypotenuse} \\sin O=\dfrac{3}{\sqrt{13}} \\ Rationalizing\\sin O=\dfrac{3\sqrt{13}}{13}$

$cos O=\dfrac{Adjacent}{Hypotenuse} \\cos O=\dfrac{2}{\sqrt{13}} \\ Rationalizing\\cos O=\dfrac{2\sqrt{13}}{13}$

$Tan O=\dfrac{Opposite}{Adjacent} \\tan O=\dfrac{3}{2}$