1 Pre-­‐Calculus Name: _______________________ Wkst 4.5 Day 3 ~ REVIEW sec, csc, tan, cot Matching. A. B. 1. y = tan x 2. y = cot x 3. y = sec x C. D. 4. y = csc x Determine the period, amplitude, vertical shift, and phase shift of each. (Do NOT graph) 1⎞
⎛t π⎞
⎛
5. y = −5tan (3x − π ) 6. y = 5 csc ⎜ 3π x − ⎟ + 3 7. y = sec ⎜ + ⎟ ⎝
⎝3 4⎠
2⎠
Amp = __________ Amp = __________ Amp = __________ Per = ___________ Per = ___________ Per = ___________ V.S. = ___________ V.S. = ___________ V.S. = ___________ P.S. = ___________ P.S. = ___________ P.S. = ____________ Graph two periods of each equation. Label your axes appropriately. PLOT points, not just a rough sketch! 8. y = −2 tan(2x) 9. y = −sec(π x) ⎛ πx⎞
10. y = csc ( 2x − π ) 11. y = cot ⎜ ⎟ ⎝ 6 ⎠
⎛ πx⎞
12. y = 2sec ⎜ ⎟ + 1 13. y = tan ( 2x − π ) ⎝ 3⎠
Application Problems. 14. The Bolivar Lighthouse located on a small island 350 ft from the shore of the mainland as shown. a.) Express the distance d as a function of the angle x. b.) If x is 1.55 rad, what is d? 15. A hot-­‐air balloon over New Mexico is being blown east from point P and traveling at a constant height of 800 ft. The angle y is formed by the ground and the line of vision from P to the balloon. This angle changes as the balloon travels. a.) Express the horizontal distance x as a function of the angle y. b.) When the angle is π/20 rad, what is the distance from P? c.) An angle of π/20 rad is how many degrees?