1. Graphing Tangent and the Reciprocal Functions

2. Graphing Tangent y = tan x = sin x cos x
y undefined when cos x = 0, so at π/2, 3π/2, 5π/2… and also at - π/2, - 3π/2, -5π/2, etc.
y equal to 0 when sin x = 0, so at 0, π, 2π… and also at -π, -2π, etc.
y equal to 1 at π/4 and -1 at –π/4

3. It continues increasing as approaching π/2 and decreasing as approaching -π/2 . Period? When does it start repeating? Now graph this!

4. y = tan x

5. Summary of Tangent Graph
Domain all reals but ±π/2, ±3π/2, ±5π/2… Range all reals Period π Asymptotes x = ±π/2, x = ±3π/2 … Intercepts 0, ±π, ±2π, ±3π

6. Now graph these with your partner.
y = -tan (x – π/4)
y = tan (x/2)

7. Graph y = cot x

8. Graph y = -1/2 cot πx

9. Graph y = csc x

10. Graph y = 4secπx