Question

(10.02)

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:

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

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

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