1. Section 4.6 Graphs of Other Trigonometric Functions
MA.PC Define and graph trigonometric functions (i.e.,sine, cosine, tangent, cosecant, secant, cotangent).
MA.PC Find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions.
MA.PC Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift.

2. Graph of y=tan x

3. The Tangent Curve Period: π
Notice that the graph passes through -1 a quarter of the way through the period and 1 at three quarters of the way.
Period: π
Domain: All real numbers except odd multiples of π/2
Range: All real numbers
Vertical asymptotes: at odd multiples of π/2
Point out that it goes through (1,pi/4) and (-1, -pi/4)

4. Graphing y = A tan(Bx + C) + D
Vertical Shift = D: Moves the midline
Amplitude = |A|: Tangent crosses the amplitude (max and min lines) at ¼ and3/4 of the way between the asymptotes
Period = /B: An asymptote occurs at /2B
Phase Shift = -C/B: Shifts graph right or left

5. Example Graphs

6. Example

7. Example

8. The Cotangent Curve Period: π
Notice the graph passes through 1 a quarter of the way through the period and -1 at three quarters of the way.
Period: π
Domain: All real #s except integral multiples of π
Range: All real numbers
Vertical asymptotes: at integral multiples of π

9. Notice the relationship to sin x
The Cosecant Curve
Notice the relationship to sin x
Period: 2π
Domain: All real #s except integral multiples of π
Range: (-∞,-1]U[1,∞]
Vertical asymptotes: at integral multiples of π

10. Notice the relationship to cos x
The Secant Curve
Notice the relationship to cos x
Period: 2π
Domain: All real numbers except odd multiples of π/2
Range: (-∞,-1]U[1,∞]
Vertical asymptotes: at odd multiples of - π/2

11. Example

12. Example

13. The Six Curves of Trigonometry

14. Graphs of the six trig functions

15. Graphs of the six trig functions

16. Review
(a)
(b)
(c)
(d)

17. Review
(a)
(b)
(c)
(d)

18. Homework
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