f ( x ) = sin ⁡ 4 3 ( x + 3 π 2 ) + 2 f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2 f ( x ) = sin 3 4 ( x + 2 3 π ) + 2 Find the amplitude.

left 3 π 2 \frac{3\pi}{2} 2 3 π

f ( x ) = sin ⁡ 4 3 ( x + 3 π 2 ) + 2 f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2 f ( x ) = sin 3 4 ( x + 2 3 π ) + 2 Find the phase shift.

left 3 π 2 \frac{3\pi}{2} 2 3 π

right 3 π 2 \frac{3\pi}{2} 2 3 π

f ( x ) = sin ⁡ 4 3 ( x + 3 π 2 ) + 2 f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2 f ( x ) = sin 3 4 ( x + 2 3 π ) + 2 Find the vertical shift.

right 3 π 2 \frac{3\pi}{2} 2 3 π

left 3 π 2 \frac{3\pi}{2} 2 3 π

f ( x ) = − 2 cos ⁡ 2 ( x + 5 π 4 ) + 3 f\left(x\right)=-2\cos2\left(x+\frac{5\pi}{4}\right)+3 f ( x ) = − 2 cos 2 ( x + 4 5 π ) + 3 Find the phase shift.

left 5 π 4 \frac{5\pi}{4} 4 5 π

right 5 π 4 \frac{5\pi}{4} 4 5 π

f ( x ) = − 2 cos ⁡ 2 ( x + 5 π 4 ) + 3 f\left(x\right)=-2\cos2\left(x+\frac{5\pi}{4}\right)+3 f ( x ) = − 2 cos 2 ( x + 4 5 π ) + 3 Find the vertical shift.

left 5 π 4 \frac{5\pi}{4} 4 5 π

right 5 π 4 \frac{5\pi}{4} 4 5 π

f ( x ) = 2 sec ⁡ 2 ( x + 3 π 4 ) + 1 f\left(x\right)=2\sec2\left(x+\frac{3\pi}{4}\right)+1 f ( x ) = 2 sec 2 ( x + 4 3 π ) + 1 Find the phase shift.

left 3 π 4 \frac{3\pi}{4} 4 3 π

right 3 π 4 \frac{3\pi}{4} 4 3 π

f ( x ) = 2 sec ⁡ 2 ( x + 3 π 4 ) + 1 f\left(x\right)=2\sec2\left(x+\frac{3\pi}{4}\right)+1 f ( x ) = 2 sec 2 ( x + 4 3 π ) + 1 Find the vertical shift.

right 3 π 4 \frac{3\pi}{4} 4 3 π

left 3 π 4 \frac{3\pi}{4} 4 3 π

Transformations of Trigonometric Functions

Authored by Joan Barrera

Mathematics

10th - 12th Grade

CCSS covered

Used 56+ times

Transformations of Trigonometric Functions

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26 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Find the period
$f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$

$\frac{1}{2}$

-1

4 $\pi$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the amplitude.
$f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$

$\frac{1}{2}$

-1

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the phase shift.
$f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$

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

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

up 1

down 1

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the vertical shift.
$f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$

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

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

up 1

down 1

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$

Find the amplitude.

$\frac{3\pi}{2}$

left $\frac{3\pi}{2}$

up 2

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$
Find the period.

$\frac{4}{3}$

$\frac{3\pi}{2}$

up 2

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$
Find the phase shift.

right $\frac{3\pi}{2}$

left $\frac{3\pi}{2}$

up 2

down 2

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$
Find the vertical shift.

right $\frac{3\pi}{2}$

left $\frac{3\pi}{2}$

up 2

down 2

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$f\left(x\right)=\frac{3}{2}\cos\ \frac{2}{3}\left(x-\frac{\pi}{4}\right)$
Find the amplitude

$\frac{3}{2}$

$\frac{2}{3}$

$\frac{\pi}{4}$

Tags

CCSS.HSF-IF.C.7E

10.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$f\left(x\right)=\frac{3}{2}\cos\ \frac{2}{3}\left(x-\frac{\pi}{4}\right)$
Find the period.

$\frac{3}{2}$

3 $\pi$

$\frac{2}{3}$

$\frac{\pi}{4}$

Tags

CCSS.HSF-IF.C.7E

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Transformations of Trigonometric Functions

Find the period f(x)=cos⁡ 12(x−π2)−1f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1f(x)=cos 21​(x−2π​)−1

Find the amplitude. f(x)=cos⁡ 12(x−π2)−1f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1f(x)=cos 21​(x−2π​)−1

Find the phase shift. f(x)=cos⁡ 12(x−π2)−1f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1f(x)=cos 21​(x−2π​)−1

Find the vertical shift. f(x)=cos⁡ 12(x−π2)−1f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1f(x)=cos 21​(x−2π​)−1

f(x)=sin⁡ 43(x+3π2)+2f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2f(x)=sin 34​(x+23π​)+2 Find the amplitude.

f(x)=sin⁡ 43(x+3π2)+2f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2f(x)=sin 34​(x+23π​)+2 Find the period.

f(x)=sin⁡ 43(x+3π2)+2f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2f(x)=sin 34​(x+23π​)+2 Find the phase shift.

f(x)=sin⁡ 43(x+3π2)+2f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2f(x)=sin 34​(x+23π​)+2 Find the vertical shift.

f(x)=32cos⁡ 23(x−π4)f\left(x\right)=\frac{3}{2}\cos\ \frac{2}{3}\left(x-\frac{\pi}{4}\right)f(x)=23​cos 32​(x−4π​) Find the amplitude

f(x)=32cos⁡ 23(x−π4)f\left(x\right)=\frac{3}{2}\cos\ \frac{2}{3}\left(x-\frac{\pi}{4}\right)f(x)=23​cos 32​(x−4π​) Find the period.

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Discover more resources for Mathematics

Find the period
$f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$

Find the amplitude.
$f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$

Find the phase shift.
$f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$

Find the vertical shift.
$f\left(x\right)=\cos\ \frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$

$f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$

Find the amplitude.

$f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$
Find the period.

$f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$
Find the phase shift.

$f\left(x\right)=\sin\ \frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$
Find the vertical shift.

$f\left(x\right)=\frac{3}{2}\cos\ \frac{2}{3}\left(x-\frac{\pi}{4}\right)$
Find the amplitude

$f\left(x\right)=\frac{3}{2}\cos\ \frac{2}{3}\left(x-\frac{\pi}{4}\right)$
Find the period.