Fill in the blank Let theta be an angle in standard position

Fill in the blank. Let theta be an angle in standard position, with (x, y) a point on the terminal side of theta and r = Squareroot x^2 + y^2 notequalto 0. x/r =

Solution

We have given r=sqrt(x²+y²)-------(1)

An angle in standard position is an angle lying in the Cartesian plane whose vertex is at the origin and whose initial ray lies along the positive x-axis.

both side square the equation (1)

r²=x²+y²

x/r =cos(theta)

since the above equation is equal to right triangle formula:

sin(theta)=y/r and cos(theta)=x/r    x is adjacent side    r is hypotenuse    y is opposite side

=opposite side /hypotenuse