Evaluate the values of the six trigonometric functions at each of the following angles. If the value does not exist, write “undefined.” (a) sinp 6 = cscp 6 = cosp 6 = secp 6 = tanp 6 = cotp 6 = (b) sin� - 5p 3 ? = csc� - 5p 3 ? = cos� - 5p 3 ? = sec� - 5p 3 ? = tan� - 5p 3 ? = cot� - 5p 3 ? = (c) sin(495? ) = csc (495? ) = cos (495? ) = sec (495? ) = tan(495? ) = cot(495? ) = 2. Given that cos(?) = - 4 5 and that csc(?) < 0,="" construct="" a="" reference="" triangle="" and="" use="" it="" to="" compute="" the="" values="" of="" all="" other="" trigonometric="" functions="" of="">
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Worksheet #2 MATH U127: Precalculus II 7/11 Name: Directions: 1) You must write up your solutions individually. 2) Show all work for full credit. 3) Clearly indicate your ?nal answer. 4) Each question is worth 3 points for a total of 15 points. This worksheet is due onTuesday, July 18th at8:00am. 1. Evaluatethevalues ofthesix trigonometricfunctions ateachof thefollowing angles. If the value does not exist, write “unde?ned.” � ? � ? 5 5 sin = csc = sin = csc = 6 6 3 3 � ? � ? 5 5 (a) (b) cos = sec = cos = sec = 6 6 3 3 � ? � ? 5 5 tan = cot = tan = cot = 6 6 3 3 sin(495 )= csc(495 )= (c) cos(495 )= sec(495 )= tan(495 )= cot(495 )= 4 2. Given that cos() = and that csc()<>
Worksheet #2 MATH U127: Precalculus II 7/11 Name: Directions: 1) You must write up your solutions individually. 2) Show all work for full credit. 3) Clearly indicate your final answer. 4) Each question is worth 3 points for a total of 15 points. This worksheet is due on Tuesday, July 18th at 8:00am. 1. Evaluate the values of the six trigonometric functions at each of the following angles. If the value does not exist, write “undefined.” (a) sin �π 6 � = csc �π 6 � = cos �π 6 � = sec �π 6 � = tan �π 6 � = cot �π 6 � = (b) sin − 5π 3 = csc − 5π 3 = cos − 5π 3 = sec − 5π 3 = tan − 5π 3 = cot − 5π 3 = (c) sin (495◦) = csc (495◦) = cos (495◦) = sec (495◦) = tan (495◦) = cot (495◦) = 2. Given that cos(θ ) = − 4 5 and that csc(θ ) < 0, construct a reference triangle and use it to compute the values of all other trigonometric functions of θ . 3. a ferris wheel is built such that the height h (in feet) above ground of a seat on the wheel at time t (in seconds) can be modeled by h(t) = 53+ 50sin � π 10 t − π 2 � . (a) what is the period of the function which models the height? give units. briefly explain what the period tells you about the ride. (b) what is the amplitude of the function which models the height? give units. briefly explain what the amplitude tells you about the ride. (c) what is the vertical shift of the function which models the height? give units. briefly explain what the vertical shift of the function tells you about the ride. 4. for each of the following transformations of the sine and cosine functions, determine (i) the amplitude, (ii) the period, (iii) the horizontal (phase) shift, (iv) whether the graph is reflected across the x-axis, (v) the vertical shift, and (vi) where the five key points from the original graph end up. then graph two full periods of the function on the blank axes provided. (a) y = 3cos � x − π 4 � − 2 (b) y = −2sin (2πx + 6π) + 3 5. for each of the following transformations of the other trigonometric functions, determine (i) the period, (ii) the horizontal shift, (iii) whether the graph is reflected across the x-axis, and (iv) the vertical shift. then graph two full periods of the function on the blank axes provided. sketch any vertical asymptotes on your graph. (a) y = − tan (πx − 5π) (b) y = csc (3x −π) + 1 0,="" construct="" a="" reference="" triangle="" and="" use="" it="" to="" compute="" the="" values="" of="" all="" other="" trigonometric="" functions="" of="" θ="" .="" 3.="" a="" ferris="" wheel="" is="" built="" such="" that="" the="" height="" h="" (in="" feet)="" above="" ground="" of="" a="" seat="" on="" the="" wheel="" at="" time="" t="" (in="" seconds)="" can="" be="" modeled="" by="" h(t)="53+" 50sin="" �="" π="" 10="" t="" −="" π="" 2="" �="" .="" (a)="" what="" is="" the="" period="" of="" the="" function="" which="" models="" the="" height?="" give="" units.="" briefly="" explain="" what="" the="" period="" tells="" you="" about="" the="" ride.="" (b)="" what="" is="" the="" amplitude="" of="" the="" function="" which="" models="" the="" height?="" give="" units.="" briefly="" explain="" what="" the="" amplitude="" tells="" you="" about="" the="" ride.="" (c)="" what="" is="" the="" vertical="" shift="" of="" the="" function="" which="" models="" the="" height?="" give="" units.="" briefly="" explain="" what="" the="" vertical="" shift="" of="" the="" function="" tells="" you="" about="" the="" ride.="" 4.="" for="" each="" of="" the="" following="" transformations="" of="" the="" sine="" and="" cosine="" functions,="" determine="" (i)="" the="" amplitude,="" (ii)="" the="" period,="" (iii)="" the="" horizontal="" (phase)="" shift,="" (iv)="" whether="" the="" graph="" is="" reflected="" across="" the="" x-axis,="" (v)="" the="" vertical="" shift,="" and="" (vi)="" where="" the="" five="" key="" points="" from="" the="" original="" graph="" end="" up.="" then="" graph="" two="" full="" periods="" of="" the="" function="" on="" the="" blank="" axes="" provided.="" (a)="" y="3cos" �="" x="" −="" π="" 4="" �="" −="" 2="" (b)="" y="−2sin" (2πx="" +="" 6π)="" +="" 3="" 5.="" for="" each="" of="" the="" following="" transformations="" of="" the="" other="" trigonometric="" functions,="" determine="" (i)="" the="" period,="" (ii)="" the="" horizontal="" shift,="" (iii)="" whether="" the="" graph="" is="" reflected="" across="" the="" x-axis,="" and="" (iv)="" the="" vertical="" shift.="" then="" graph="" two="" full="" periods="" of="" the="" function="" on="" the="" blank="" axes="" provided.="" sketch="" any="" vertical="" asymptotes="" on="" your="" graph.="" (a)="" y="−" tan="" (πx="" −="" 5π)="" (b)="" y="csc" (3x="" −π)="" +="">