How do you sketch the angle whose terminal side in standard position passes through #(1,sqrt3)# and how do you find sin and cos?

1 Answer
Feb 9, 2018

Answer:

#sin(x) = y/(Hyp) = sqrt(3)/2# and #cos(x)=x/(Hyp) = 1/2#

Explanation:

If you place the triangle on a graph, with one side laying on the positive side of the x-axis, and set the other side to pass through the origin and the given point #(1, sqrt(3))# it will form a right triangle.

The bottom side will be the "adjacent" side to the angle, while the vertical side is the "opposite."

knowing the acronym SOH CAH TOA
#sin=(Opposite)/(Hypotenuse)# , #cos=(Adjacent)/(Hypotenuse)# , #tan=(Opposite)/(Adjacent)#

and the Pythagorean Theorem
#(Hypotenuse)^2 = (Opposite)^2 + (Adjacent)^2#

We can find that
#Hyp^2 = (sqrt(3))^2 + 1^2#
By solving for Hyp, we see that the hypotenuse is 2 units long.

Knowing this, we can then solve the sine and cosine.