How do you find #sintheta# and #costheta# if the terminal side of #theta# lies along the line #y=2x# in QI?

1 Answer
Douglas K.
Apr 29, 2018

The slope, m, of the line #y = 2x# is, #m =2#.

For this line, we know that any ordered pair of coordinates will form a right triangle, therefore, we can choose any point and use the Pythagorean Theorem to compute the hypotenuse:

#h^2 = x^2+y^2#

Let's choose the point #(1,2)#:

#h^2 = 1^2+2^2#

#h^2 = 1+4#

#h^2 = 5#

#h = sqrt5#

We know that:

#sin(theta) = y/h#

#sin(theta) = 2/sqrt5#

Rationalize the denominator:

#sin(theta) = 2sqrt5/5#

We know that:

#cos(theta) = x/h#

#cos(theta) = 1/sqrt5#

Rationalize the denominator:

#cos(theta) = sqrt5/5#

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