Chapter 2 Trigonometric Functions of Real Numbers Section 2.2 Trigonometric Functions of Real Numbers

Trigonometric Functions If t is a real number that is the length of an arc on the unit circle and P is a point at the end of that arc with coordinates ( x,y ) then we get the following expressions for each of the trigonometric ratios: P ( x,y ) 1 t Find the values of the trigonometric functions at t =  /6. 1

Find the values of the trigonometric functions at t = 3  / This concept for the trigonometric functions agrees with what we learned about the trigonometric ratios. This is a special case where the point on the terminal side of the angle in standard position is on the unit circle. Notice x is the length of the adjacent side and y is the length of the opposite side and the hypotenuse is of length 1.

The values of the trigonometric functions will be the same as that of the trigonometric ratios. In particular for the angles 0,  /6,  /4,  /3,  /2 (i.e. 0°,30°,45°,60°,90°). In the picture to the right the first quadrant is shown along with the terminal points on the unit circle

Reciprocal Identities: Even & Odd Properties Changing the direction of the angle from clockwise to counterclockwise or visa versa makes no difference to the cosine and secant, they are called even functions. The sine, tangent, cotangent and cosecant a change in direction makes them the negative of what they were.

Pythagorean Identities: These can be very useful when trying to do the following problem. If t is an angle in the second quadrant and sin t = 5/6 find the other trigonometric functions of t. second quadrant cos is negative