To find the value of cosine when α = 3π/2, we can use the unit circle to determine the angle in standard position that terminates with a reference angle of π/2 (90 degrees) in the third quadrant.
In the third quadrant, cosine is negative. Since cosine is adjacent/hypotenuse, and the radius of the unit circle is 1, we can use the Pythagorean theorem to find the adjacent side length.
Let x be the adjacent side length, and let r be the radius of the unit circle (which is 1).
We know that: x^2 + 1^2 = 1^2 x^2 + 1 = 1 x^2 = 0 x = 0
To find the value of cosine when α = 3π/2, we can use the unit circle to determine the angle in standard position that terminates with a reference angle of π/2 (90 degrees) in the third quadrant.
In the third quadrant, cosine is negative. Since cosine is adjacent/hypotenuse, and the radius of the unit circle is 1, we can use the Pythagorean theorem to find the adjacent side length.
Let x be the adjacent side length, and let r be the radius of the unit circle (which is 1).
We know that:
x^2 + 1^2 = 1^2
x^2 + 1 = 1
x^2 = 0
x = 0
Since x = 0, the cosine of 3π/2 is 0.
Therefore, cos(3π/2) = 0.