Free Essays on Trig

Take an x-axis and an y-axis (orthonormal) and let o be the origin. A circle centered in o and with radius = 1, is called a trigonometric circle or unit circle. Turning counterclockwise is the positive orientation in trigonometry. Angles are measured starting from the x-axis. Two units to measure an angle are degrees and radians An orthogonal angle = 90 degrees = pi/2 radians In this theory we use mainly radians. With each real number t corresponds just one angle, and just one point p on the unit circle, when we start measuring on the x-axis. We call that point the image point of t. Examples: with pi/6 corresponds the angle t and point p on the circle. with -pi/2 corresponds the angle u and point q on the circle. Trigonometric numbers of a real number t With t radians corresponds exactly one point p on the unit circle. The x-coordinate of p is called the cosine of t. We write cos(t). The y-coordinate of p is called the sine of t. We write sin(t). The number sin(t)/cos(t) is called the tangent of t. We write tan(t). The number cos(t)/sin(t) is called the cotangent of t. We write cot(t). The number 1/cos(t) is called the secant of t. We write sec(t) The number 1/sin(t) is called the cosecant of t. We write csc(t) The line with equation sin(t).x - cos(t).y = 0 contains the origin and point p(cos(t),sin(t)). So this line is op. On this line we take the intersection point s(1,?) with the line x=1. It is easy to see that ? = tan(t). So tan(t) is the y-coordinate of the point s. Analogous cotan(t) is the x-coordinate of the intersection point s' of the line op with the line y=1. Basic formulas With t radians corresponds exactly one point p(cos(t),sin(t)) on the unit circle. The square of the distance [op] = 1. Calculating this distance with the coordinates of p we have for each t : cos ²(t) + sin ²(t) = 1 sin ²(t) cos ²(t)+sin ²(t) 1... Free Essays on Trig Free Essays on Trig Take an x-axis and an y-axis (orthonormal) and let o be the origin. A circle centered in o and with radius = 1, is called a trigonometric circle or unit circle. Turning counterclockwise is the positive orientation in trigonometry. Angles are measured starting from the x-axis. Two units to measure an angle are degrees and radians An orthogonal angle = 90 degrees = pi/2 radians In this theory we use mainly radians. With each real number t corresponds just one angle, and just one point p on the unit circle, when we start measuring on the x-axis. We call that point the image point of t. Examples: with pi/6 corresponds the angle t and point p on the circle. with -pi/2 corresponds the angle u and point q on the circle. Trigonometric numbers of a real number t With t radians corresponds exactly one point p on the unit circle. The x-coordinate of p is called the cosine of t. We write cos(t). The y-coordinate of p is called the sine of t. We write sin(t). The number sin(t)/cos(t) is called the tangent of t. We write tan(t). The number cos(t)/sin(t) is called the cotangent of t. We write cot(t). The number 1/cos(t) is called the secant of t. We write sec(t) The number 1/sin(t) is called the cosecant of t. We write csc(t) The line with equation sin(t).x - cos(t).y = 0 contains the origin and point p(cos(t),sin(t)). So this line is op. On this line we take the intersection point s(1,?) with the line x=1. It is easy to see that ? = tan(t). So tan(t) is the y-coordinate of the point s. Analogous cotan(t) is the x-coordinate of the intersection point s' of the line op with the line y=1. Basic formulas With t radians corresponds exactly one point p(cos(t),sin(t)) on the unit circle. The square of the distance [op] = 1. Calculating this distance with the coordinates of p we have for each t : cos ²(t) + sin ²(t) = 1 sin ²(t) cos ²(t)+sin ²(t) 1...