Trigonometry can be studied using two different approaches. The first approach makes usse of circular functions which involve angles and angle rotations, extended to include th definitions of trigonometric functions based on the unit circle. With the real numbers as the domain, the periodic functions are defined in terms of the unit circle. The second aaproach makes use of the trigonometric functions to study triangles and their applications.
An angle is formed by two rays with a common endpoint. One side of the angle rotates about the common endpoint and the other side remains stationary. The stationary ray is the initial side of the angle and the rotating ray is the terminal side. The angle formed by the rotating he terminal side exactly once in the counterclockwise direction until it coincides with the initial side has a degree measure of 360(1 revolution). Revolution is the motion of the bodyabout a center or about its axis. One degree is equal to 1/360 revolution.
If the terminal side of a central angle coincides with the coordinate axis such that its initial side coincides with the positive side of the x-axis the angle is called quadrantal angle.
Radian is the measure of a central angle of a circle whose rays subtend an arc on the circle whose length is equal to the radius of the circle.
The length of an arc of a circle of radius r subtended by a central angle theta is given by the product of radius and the measure of the central angle in radians. That is, s=r(theta)
The reference angle for a nonquadrantal angle greater than 90 degrees is the smallest nonnegative angle between the terminal side and the x-axis when the angle is in standard position.
Unit Circle
Trigonometric Functions and Identities
The major functions where the trigonometric functions are based or formed by using the abscissa, ordinate, and the radius vector of a point on the terminal side of an angle in standard position.
sin theta= ordinate/radius vector= y/r
cos theta= abscissa/radius vector= x/r
tan theta= ordinate/abscissa= y/x, where x is not equal to 0
csc theta= radius vector/ordinate= r/y
sec theta= radius vector/abscissa = r/x
cot theta= abscissa/ordinate= x/y, where y is not equal to 0
When an equality is true for all values of the uknown quantity or quantities, the equality is called an ientity. By means of proveen idntities, it is possible to prove other identities.
sin2theta+cos2theta=1
tantheta= sintheta/costheta
cot theta= costheta/sintheta
sectheta= 1/costheta
csctheta= 1/sintheta
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