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? Make sure to show all work.

Answer 1

`Sin \theta = (Perpendicular)/(Hypotenuse)=(3)/(√(13))`

`Cos \theta = (Base)/(Hypotenuse)=(2)/(√(13))`

`Tan \theta = (Perpendicular)/(Base)=(3)/(2)`

Explanation:

We are given that The point (2, 3) is on the terminal side of angle Θ, in standard position

First Draw a vertical line from the point(2,3) to the x axis.

So, Length of vertical line is 3

The intersection of the line with the x axis is at x=2.

So, now we have obtained a triangle with the horizontal side of length 2, the vertical side of length 3

To Find hypotenuse we will use Pythagoras theorem

`Hypotenuse^2=Perpendicular^2+Base^2\\Hypotenuse^2=3^2+2^2\\Hypotenuse=√(9+4)\\Hypotenuse=√(13)`

`Sin \theta = (Perpendicular)/(Hypotenuse)=(3)/(√(13))`

`Cos \theta = (Base)/(Hypotenuse)=(2)/(√(13))`

`Tan \theta = (Perpendicular)/(Base)=(3)/(2)`