The trigonometric functions sine, cosine and tangent calculate the ratio of two sides in a right triangle when given an angle in that triangle. To find the cosine of angle pi, you need graph paper.
Continue ReadingUse a sheet of graph paper that already has a vertical, or y, and a horizontal, or x, axis or draw them. To the right of the y-axis, x is positive, and above the x-axis, y is positive. Mark the right side of the x axis as "0, 2pi" in radians, meaning that the ray starting at the origin and extending horizontally to the right is at angle 0. It is also 2pi, because in radians, 2pi is a complete circle. Angle pi is half of 2pi, meaning that it is halfway around the circle. Halfway around the circle is along the same horizontal line but in the opposite direction. Label the left side of the x-axis pi.
Every point on an x-y plot creates a right triangle whose height extends vertically to the x-axis and whose hypotenuse extends to the origin. At any point along the left-pointing ray, the triangle has no height. The cosine is the ratio of the adjacent side and the hypotenuse. At point (-10,0), for example, both the adjacent and hypotenuse have an absolute value of 10. The fraction 10/10 equals 1. At any point along the ray, the ratio is still 1:1.
The result of a cosine function is negative when the triangle is left of the y axis or when x is negative. A negative number divided by a positive number is negative, and the hypotenuse is always positive. cos(pi) = -1/1 = -1