Strawser PreCalc Ch 4.4-4.6 practice questions
sec (fancy 0)
= 1/cos
csc (fancy 0)
= 1/sin
Tan (fancy 0)
= sin/cos
Cot (fancy 0)
=cos/sin
Write an equation for the following graph. Choose the correct answer. A. y=4tan (x+π/6) B. y=4tan 2(x−π/6) C. y=−4tan (x+π/6) D. y=-4tan 2(x−π/6)
A. y=4tan (x+π/6)
Find an equation of the graph shown on the right. Choose the correct equation. The graph crosses the x-axis at points pi/2 and 3pi/2 It also has 2 points that are (3pi/4, 5) and (5pi/4, -5)
A. y=5sin(x−π/2) B. y=5sin(2x−π/2) C. y=10sin(2x−π) D. y=5sin(2x-π)<-CORRECT ANSWER
Write an equation for the graph. Choose the correct equation below. A. y=3sec(2x) B. y=5sin(3x) C. y=2csc(3x) D. y=6cos(x−π/2) E. y=5csc[3(x+π)] F. y=5csc[6(x+π)]
C. y=2csc(3x)
Write the following function in the form y=acosb(x−c). Find the period and phase shift. y=4/3cos(π/6x−π/6) Write the given function in the form y=acosb(x−c). A. y=4/3cos6(x−π) B. y=2π/9cos(x−π) C.y=4/3cosπ6(x−1) D. y=2π/9cos(x−1)
C.y=4/3cosπ6(x−1) The period is 12. The phase shift is 1.
Type the equation of the given graph in the form y=AsinBx or y=AcosBx. y=4 sine 1/2 x
Crosses (0,0) X-axis is -2pi, (0,0), 2pi, 4pi The y goes up to 4 and down to 4 but the x that goes with it is pi
Write the following function in the form y=asinb(x−c). Find the period and phase shift. y=−54sin(4x−π) Write the given function in the form y=asinb(x−c). A. y=−5sin(x−π) B. y=−5sin(x−π/4) C.y=−5/4sin[4(x−π)] D. y=−5/4sin[4(x−π/4)]
D. y=−5/4sin[4(x−π/4)] <-CORRECT ANSWER The period is π/2. The phase shift is π/4.
Sketch the graph of the given equation over the interval [−2π, 2π]. y=sin 5/6 x
Graph goes through (0,0) Has a low point in the negatives thats y is -1 and has a high point in the positives thats y is 1 Can not really tell what the xs are but my guess is its something close to 5/6
Graph the following function over a one-period interval. y=−2sin(x−π/2)
Graph has y-intersect of 2 Crosses the x-axis between -pi and 0 and also 0 and pi and again a third time between 2pi and 3pi One of the apparent points are (pi, -2)
Sketch the graph of the given equation over the interval [−2π, 2π]. y=cos(x−π/10)
Graph just barely misses having the y-intercept of 1 Has two low points. Don't know the x-intercepts
Graph the function over a one-period interval. y=tanx+π/8
Graph starts in quad with all negative and goes to all positives With points (-3pi/8, -1) and (pi/8, 1) With asymptotes of -5pi/8 and 3pi/8
Sketch the graph of the given equation over the interval [−2π, 2π]. y=sin(x+pi/12)
Graphs y points coincide with 1 and -1 Just barely miss the x points of -pi and pi
Phase shift- (horizontal translation, new center, moves left and right) Amplitude- (height up and down, the y coordinate on some points) Period- (what you add 1/4 to to get your points)
PS- on a graph how it is shifted horizontally Amp- x axis to the highest point (so technically the max) Per- length of one cycle of the curve to the next 2pi/B or 360degrees/B except for tan and cot they are 180degrees/B or pi/B
SOHCAHTOA
SIN (Opposite/Hypotenuse) COS (Adjacent/Hypotenuse) TAN (Opposite/Adjacent)
Find the amplitude, period, and phase shift of the following function. y=−2sin[1/2(x+π/2)]
The amplitude is 2. The period is 4π. The phase shift is −π/2.
Find the amplitude, period, and phase shift of the given function. y=−3sin(x+2π)
The amplitude is 3. The period is 2π. The phase shift is −2π.
The domain of f(x)=sin−1x is __________.
The domain of f(x)=sin−1x is [−1,1].
Sketch the graph of the given equation over the interval [−2π, 2π]. y=7cosx
The graph crosses y-axis at positive 7 (this is at a max) Crosses the x-axis in the middle of pi and 2pi and also in the middle of -pi and -2pi Starts high, has a low dip, has the high dip(max) at the positive 7, goes back down for a low dip and back up
Find the period and the phase shift of the function y=3sin(4x−π/2).
The period of the function is π/2 and the phase shift of the function is π/8.
The range of f(x)=tan−1x is __________.
The range of f(x)=tan−1x is (−π/2,π/2)
The tangent function has period __________.
The tangent function has period π.
State whether the following statement is true or false. If −1≤x≤0, then sin−1x≤0. Choose the correct answer below. True False
True
Sketch the graph of the given equation over the interval [−2π, 2π]. y=sinx−8 Select all the transformations that are needed to graph the given function using y=sinx.
a. Graph was originally squiggly line. But now its squiggly line that crosses the y axis at -8 b. Shift the graph down 8 units.
The voltage across the terminals of a typical electrical outlet is approximated by V(t)=142sin(160πt), where t is measured in seconds. Answer parts (a) through (c). (a) Find the amplitude and the period for V(t). (b) Find the frequency of V(t), that is, the number of cycles completed in one second. (c) Graph V(t) over the interval [0, 1/40]
a. The amplitude of the voltage is 142. And the period of the voltage is 1/80. b. The frequency of V(t) is 80.
On the graphing tool if graphing cos use the graph button that looks like ______. If graphing sine use the one that looks like _____.
cos- up, down, up (usually starts at (0,1), starts at a max and ends at a max) sine- half an infinity sign, or a really scary rollercoaster, or a double sided candy cane
Find the exact value of the expression or state that it does not exist. cos−1(cos π/10) (pi/10 is in range so= pi/10)
cos−1cosπ10=pi/10
Find the exact value, in radians, of y or state that y is undefined. y=cot−1(−square root of 3/3)
cot−1(−square root of 3/3)= 2π/3
Sec= Tan= Sin= Cos= Csc= Cot=
sec=r/x tan=y/x sin=y/r cos=x/r csc=r/y cot=x/y
Find the exact value of y, or state that y is undefined. y=sin−1(0)
sin−1(0)=0
Find the exact value of sin−1(sin 7π/6).
sin−1(sin 7π/6)=−π/6
Find the exact value of the following expression, if possible. Do not use a calculator. sin−1(sin π)
sin−1(sin π)=0
Find the exact value of y, or state that y is undefined. y=sin−1(−1/2)
sin−1(−1/2)=−π/6
Find the exact value of sin−1(−square root of 3/2).
sin−1(−square root of 3/2)=−π/3
Find the exact value of y or state that y is undefined. y=cos−1(7π/8)
undefined
Find the exact value of y, or state that y is undefined. y=sin−1(−4)
undefined
The lowest point on the graph of y=cosx, 0≤x≤2π, occurs when x=__________.
x=π
Find the slope-intercept form of the equation of the line that passes through the point P=(−3,−5) and makes angle θ=120° with the positive x-axis.
y=(-square root 3)x-(5+3(square root 3))
Find the exact value, in radians, of y or state that y is undefined. y=cot−1(−square root of 3)
y=5π/6
Find the exact value of y or state that y is undefined. y=cos(cos−1(6/7))
y=6/7
Use a calculator to find the value of y in degrees rounded to two decimal places. (degree mode on your calculator) y=tan−1 (9)
y=83.66°
Find the exact value of y or state that y is undefined. y=tan(tan−1 (9))
y=9
Find the exact value of y or state that y is undefined. y=cos−1(−1)
y=piπ
Use a sketch to find the exact value of y. y=cos(sin−1 (1/4))
y=square root 15/4
Find the slope-intercept form of the equation of the line that passes through the point P and makes angle θ with the positive x-axis. P=(5,−1), θ=45°
y=x−6
Find the exact value, in radians, of y or state that y is undefined. y=cot−1(1)
y=π/4
Find the exact value of y or state that y is undefined. y=tan−1(square root of 3/3)
y=π/6
Use a calculator to find the value of y in radians rounded to two decimal places. (radian mode on your calculator) y=sin−1(−0.83)
y=−0.98 radians
Find the exact value of y or state that y is undefined. y=sin−1(sin 5π/3)
y=−π/3
Find the exact value, in radians, of y or state that y is undefined. y=tan−1(tan 5π/6)
y=−π/6
Use a sketch to find the exact value of z. z=cos[tan-1 (9/8)]
z=8(square root 145)/145
Use a sketch to find the exact value of z. z=tan(sec−1 (4))
z=square root of 15