1. Section 13 - 1 Secant, Cosecant, and Cotangent We will evaluate reciprocal trig functions, apply properties and solve equations with reciprocals.

2. A © 2005 – All rights reserved Melissa.Campasino@hcps.org Melissa Campasino Presentation

3. cos -1 x, sin -1 x, and tan -1 x are reflections over the y = x line cos -1 x sin -1 x tan -1 x r: 0<y<  D: -1<x<1 D: R (limited domains) D: -1<x<1

4. Circular functions also have cos x: secant of x = sec x = (cos x 00 ) sin x: cosecant of x = csc x = (sin x 00 ) tan x: cotangent of x = cot x = (sin x 00 ) recall: so

5. Example: Evaluate A. Exact: = = = B. Approximate: (calculator) x -1 historically used to avoid division by irrational #’s – used less now – WHY – used in calculus

6. Example: Evaluate A. Exact: = = = B. Approximate: (calculator) x -1 historically used to avoid division by irrational #’s – used less now – WHY – used in calculus =

7. When  = 0° to 90°, can do the reciprocal of SOH-CAH-TOA

8. The angle a ramp makes with the ground should be less than 2.5°. How long must the ramp be to reach a door with a sill 6 ft. above ground? 6 ft. 2.5° x 2 options: Why choose the csc method? = 137.6 ft.

9. function properties graph properties  cos +, sec + and cos -, sec –  cos = 0, sec undef.  cos 1  cos = sec at ±1  cos & sec - same side of axis  sec asymptote at cos = 0  closer cos is to x axis, farther away sec is  graphs intersect at y= ±1

10. similar properties to sec, translated  / 2 right tan translated  / 2 right, reflected over the y-axis

11. Practice: determine the exact and approximate values of each:  sec  cot  csc  State 3 properties that compare the secant graph to the cosine graph