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