College Algebra & Trigonometry, 2018a

384 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
(x, y) =(cosθ, sin θ)
1
y
opposite
θ x
adjacent
In the picture above we see a triangle in the first quadrant with a hypotenuse of
1. In this situation, the value of sin θ = opp
hyp = y 1
= y, which is just the y-coordinate
of the point at the top of the triangle. Correspondingly, the value of cos θ = adj
hyp =
x
1
= x, or the value of the x-coordinate of the same point.
This allows us to find the sine or cosine for what are known as the quadrantal
angles - the angles that are multiples of 90 ◦ . If we look at the unit circle (the circle
with a radius of 1), then we can see the values of the sine and cosine for these
angles.
(cos 90 ◦ , sin 90 ◦ )
(0, 1)
(cos 180 ◦ , sin 180 ◦ )
(−1, 0)
(cos 0 ◦ , sin 0 ◦ )
(1, 0)
(0, −1)
(cos 270 ◦ , sin 270 ◦ )