Write an equation for the cosine function with amplitude 3, period of 2 π 2\pi 2 π , phase shift of π \pi π , and vertical shift of 5.

y = 3 cos ⁡ ( x − π ) + 5 y=3\cos(x-\pi)+5 y = 3 cos ( x − π ) + 5

y = 5 cos ⁡ ( x − π ) + 3 y=5\cos(x-\pi)+3 y = 5 cos ( x − π ) + 3

y = 3 cos ⁡ 2 ( x − π ) + 5 y=3\cos2\left(x-\pi\right)+5 y = 3 cos 2 ( x − π ) + 5

y = 5 cos ⁡ ( 2 x − π ) + 3 y=5\cos(2x-\pi)+3 y = 5 cos ( 2 x − π ) + 3

Write the equation of a cosine graph given the following: Midline: y = 0 Amplitude = 3 Reflection over the x-axis No Phase Shift Period = π \pi π

y = − 3 cos ⁡ 2 x y=-3\cos2x y = − 3 cos 2 x

y = − 3 cos ⁡ π x y=-3\cos\pi x y = − 3 cos π x

y = − 3 cos ⁡ x y=-3\cos x y = − 3 cos x

y = 3 cos ⁡ x + 2 y=3\cos x+2 y = 3 cos x + 2

Write an equation or the graph.

y = 3 sec ⁡ 2 x y=3\sec2x y = 3 sec 2 x

y = 2 sec ⁡ x y=2\sec x y = 2 sec x

y = 3 sec ⁡ x y=3\sec x y = 3 sec x

y = 3 csc ⁡ x y=3\csc x y = 3 csc x

y = 3 csc ⁡ 2 x y=3\csc2x y = 3 csc 2 x

Which equation represents the graph below?

y = 100 cos ⁡ ( π 4 x ) − 60 y=100\cos\left(\frac{\pi}{4}x\right)-60 y = 1 0 0 cos ( 4 π x ) − 6 0

y = − 60 cos ⁡ ( π 4 x ) − 100 y=-60\cos\left(\frac{\pi}{4}x\right)-100 y = − 6 0 cos ( 4 π x ) − 1 0 0

y = − 100 cos ⁡ ( π 4 x ) − 60 y=-100\cos\left(\frac{\pi}{4}x\right)-60 y = − 1 0 0 cos ( 4 π x ) − 6 0

y = 60 cos ⁡ ( π 4 x ) − 100 y=60\cos\left(\frac{\pi}{4}x\right)-100 y = 6 0 cos ( 4 π x ) − 1 0 0

SDC PreCalculus - Graphs of Trigonometric Functions

Authored by TIFFANY GARRITY

Mathematics

9th - 12th Grade

CCSS covered

Used 79+ times

SDC PreCalculus - Graphs of Trigonometric Functions

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17 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the period of $y=-\cos3\left(x-\pi\right)-5$ ?

π/3

π/6

2π/3

2π/6

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the period of this function?

\frac{\pi}{4}

$\frac{\pi}{2}$

$\pi$

$2\pi$

Tags

CCSS.HSF.TF.A.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Determine an equation for this graph:

y=csc(x)

y=sec(x)

y=cot(x)

y= tan(x)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Determine an equation for this graph:

y=csc(x)

y=sec(x)

y=cot(x)

y= tan(x)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Write an equation for the cosine function with amplitude 3, period of $2\pi$ , phase shift of $\pi$ , and vertical shift of 5.

$y=5\cos(x-\pi)+3$

$y=3\cos(x-\pi)+5$

$y=3\cos2\left(x-\pi\right)+5$

$y=5\cos(2x-\pi)+3$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the vertical shift for $y=4\cos\frac{1}{2}\left(x+\pi\right)-2$ ?

up 2

left 2

right 2

down 2

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the phase shift for $y=4\ \cos\frac{1}{2}\left(x+\pi\right)-2?$

left $\frac{\pi}{2}$

right $\frac{\pi}{2}$

right $\pi$

left $\pi$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the period for $y=4\cos\frac{1}{2}\left(x+π\right)-2?\$

pi/2

3pi

4pi

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the amplitude for $y=4\cos\frac{1}{2}\left(x+\pi\right)-2?$

$\frac{\pi}{2}$

$\pi$

Tags

CCSS.HSF-IF.C.7E

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SDC PreCalculus - Graphs of Trigonometric Functions

What is the period of y=−cos⁡3(x−π)−5y=-\cos3\left(x-\pi\right)-5y=−cos3(x−π)−5 ?

What is the period of this function?

Determine an equation for this graph:

Determine an equation for this graph:

Write an equation for the cosine function with amplitude 3, period of 2π2\pi2π , phase shift of π\piπ , and vertical shift of 5.

What is the vertical shift for y=4cos⁡12(x+π)−2y=4\cos\frac{1}{2}\left(x+\pi\right)-2y=4cos21​(x+π)−2 ?

What is the phase shift for y=4 cos⁡12(x+π)−2?y=4\ \cos\frac{1}{2}\left(x+\pi\right)-2?y=4 cos21​(x+π)−2?

What is the period for y=4cos⁡12(x+π)−2? y=4\cos\frac{1}{2}\left(x+π\right)-2?\ y=4cos21​(x+π)−2?

What is the amplitude for y=4cos⁡12(x+π)−2?y=4\cos\frac{1}{2}\left(x+\pi\right)-2?y=4cos21​(x+π)−2?

What is the equation of the graph?

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What is the period of $y=-\cos3\left(x-\pi\right)-5$ ?

Write an equation for the cosine function with amplitude 3, period of $2\pi$ , phase shift of $\pi$ , and vertical shift of 5.

What is the vertical shift for $y=4\cos\frac{1}{2}\left(x+\pi\right)-2$ ?

What is the phase shift for $y=4\ \cos\frac{1}{2}\left(x+\pi\right)-2?$

What is the period for $y=4\cos\frac{1}{2}\left(x+π\right)-2?\$

What is the amplitude for $y=4\cos\frac{1}{2}\left(x+\pi\right)-2?$