The amplitude of either y = a sin ⁡ ( b θ ) o r y = a cos ⁡ ( b θ ) y=a\sin\left(b\theta\right)\ or\ y=a\cos\left(b\theta\right) y = a sin ( b θ ) o r y = a cos ( b θ ) is determined by __________.

∣ a ∣ \left|a\right| ∣ a ∣

∣ b ∣ \left|b\right| ∣ b ∣

2 π ∣ b ∣ \frac{2\pi}{\left|b\right|} ∣ b ∣ 2 π

The period of either y = a sin ⁡ ( b θ ) o r y = a cos ⁡ ( b θ ) y=a\sin\left(b\theta\right)\ or\ y=a\cos\left(b\theta\right) y = a sin ( b θ ) o r y = a cos ( b θ ) is determined by __________.

2 π ∣ b ∣ \frac{2\pi}{\left|b\right|} ∣ b ∣ 2 π

∣ a ∣ \left|a\right| ∣ a ∣

∣ b ∣ \left|b\right| ∣ b ∣

Check all that apply for the graph of y = − 1 4 cos ⁡ ( 2 5 θ ) y=-\frac{1}{4}\cos\left(\frac{2}{5}\theta\right) y = − 4 1 cos ( 5 2 θ ) .

Its graph is an x-axis reflection of y = cos ⁡ ( θ ) y=\cos\left(\theta\right) y = cos ( θ )

Its graph is a vertical compression of y = cos ⁡ ( θ ) y=\cos\left(\theta\right) y = cos ( θ )

its graph has a period of 10 π 10\pi 1 0 π

Its graph is a horizontal compression of y = cos ⁡ ( θ ) y=\cos\left(\theta\right) y = cos ( θ )

Its amplitude is − 1 4 -\frac{1}{4} − 4 1

Check all of the true statements about the graphs in this image.

The orange graph is vertically and horizontally compressed version of blue graph of y = cos ⁡ ( θ ) y=\cos\left(\theta\right) y = cos ( θ ) .

The period of of the blue graph is 2 π 2\pi 2 π and the period of the orange graph is π 2 \frac{\pi}{2} 2 π .

The equation of the orange graph is y = 0.5 cos ⁡ ( 4 θ ) y=0.5\cos\left(4\theta\right) y = 0 . 5 cos ( 4 θ )

The equation of the orange graph is y = − 0.5 cos ⁡ ( 4 θ ) y=-0.5\cos\left(4\theta\right) y = − 0 . 5 cos ( 4 θ )

The equation of the orange graph is y = 0.5 cos ⁡ ( π 2 θ ) y=0.5\cos\left(\frac{\pi}{2}\theta\right) y = 0 . 5 cos ( 2 π θ )

Check all of the true statements that apply to the image.

The red dotted graph shows 2 period lengths and the green graph shows 1 period length.

The amplitude of the green graph is ∣ − 2.5 ∣ = 2.5 \left|-2.5\right|=2.5 ∣ − 2 . 5 ∣ = 2 . 5 .

The green curve is an x-axis reflection of the sine wave.

The period of the green graph is 2 π 2\pi 2 π .

The green graph's equation is y = 2.5 cos ⁡ ( 4 θ ) y=2.5\cos\left(4\theta\right) y = 2 . 5 cos ( 4 θ ) .

You are graphing y = 4 sin ⁡ ( 2 θ ) y=4\sin\left(2\theta\right) y = 4 sin ( 2 θ ) . You would evenly mark and scale the x-axis with the numbers ______________________.

0 , π 4 , π 2 , 3 π 4 , π 0,\frac{\pi}{4},\frac{\pi}{2},\frac{3\pi}{4},\pi 0 , 4 π , 2 π , 4 3 π , π

0 , 1 2 , 1 , 3 4 , 2 0,\frac{1}{2},1,\frac{3}{4},2 0 , 2 1 , 1 , 4 3 , 2

0 , π 2 , π , 3 π 2 , 2 π 0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi 0 , 2 π , π , 2 3 π , 2 π

0 , π , 2 π , 3 π , 4 π 0,\pi,2\pi,3\pi,4\pi 0 , π , 2 π , 3 π , 4 π

You are graphing y = − 3 cos ⁡ ( 1 2 θ ) y=-3\cos\left(\frac{1}{2}\theta\right) y = − 3 cos ( 2 1 θ ) . You would evenly mark and scale the x-axis with the numbers ______________________.

0 , π , 2 π , 3 π , 4 π 0,\pi,2\pi,3\pi,4\pi 0 , π , 2 π , 3 π , 4 π

0 , 1 2 , 1 , 3 4 , 2 0,\frac{1}{2},1,\frac{3}{4},2 0 , 2 1 , 1 , 4 3 , 2

0 , π 2 , π , 3 π 2 , 2 π 0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi 0 , 2 π , π , 2 3 π , 2 π

0 , π 4 , π 2 , 3 π 4 , π 0,\frac{\pi}{4},\frac{\pi}{2},\frac{3\pi}{4},\pi 0 , 4 π , 2 π , 4 3 π , π

You are graphing y = 0.7 sin ⁡ ( 1 3 θ ) y=0.7\sin\left(\frac{1}{3}\theta\right) y = 0 . 7 sin ( 3 1 θ ) . You would evenly mark and scale the x-axis with the numbers ______________________.

0 , 3 π 2 , 3 π , 9 π 2 , 6 π 0,\frac{3\pi}{2},3\pi,\frac{9\pi}{2},6\pi 0 , 2 3 π , 3 π , 2 9 π , 6 π

0 , π 2 , π , 3 π 2 , 2 π 0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi 0 , 2 π , π , 2 3 π , 2 π

0 , π 4 , π 2 , 3 π 4 , π 0,\frac{\pi}{4},\frac{\pi}{2},\frac{3\pi}{4},\pi 0 , 4 π , 2 π , 4 3 π , π

0 , 1 12 , 1 6 , 1 4 , 1 3 0,\frac{1}{12},\frac{1}{6},\frac{1}{4},\frac{1}{3} 0 , 1 2 1 , 6 1 , 4 1 , 3 1

You are graphing y = − 3 cos ⁡ ( 1 2 θ ) y=-3\cos\left(\frac{1}{2}\theta\right) y = − 3 cos ( 2 1 θ ) . The first point you graph on the y-axis.

( 0 , − 3 ) \left(0,-3\right) ( 0 , − 3 )

( 0 , 3 ) \left(0,3\right) ( 0 , 3 )

( 0 , 0 ) \left(0,0\right) ( 0 , 0 )

( 0 , 1 2 ) \left(0,\frac{1}{2}\right) ( 0 , 2 1 )

For the green sine wave, the length of the orange segment represents the ______________________.

period of the wave or the length of one cycle.

Resource Library

Math

Trigonometry

Graphing Sine And Cosine

Graphing Sine And Cosine With Amplitude & Period Changes

Graphing Sine and Cosine with amplitude & period changes

Authored by Kelly Lama

Mathematics

9th Grade - University

CCSS covered

Used 33+ times

Graphing Sine and Cosine with amplitude & period changes

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Content View
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20 questions

Show all answers

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

The red curve is the graph of ______________.

$y=\cos\left(\theta\right)$

$y=\sin\left(\theta\right)$

$y=\tan\left(\theta\right)$

$x^2+y^2=r^2$

NONE of the above

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

The blue curve is the graph of ______________.

$y=\cos\left(\theta\right)$

$y=\sin\left(\theta\right)$

$y=\tan\left(\theta\right)$

$x^2+y^2=r^2$

NONE of the above

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

The amplitude of a sine or cosine wave measures the distance from the midline to the "top" of the wave, which is also the distance from the midline to the "bottom" of the wave.

True

False

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The amplitude of either $y=a\sin\left(b\theta\right)\ or\ y=a\cos\left(b\theta\right)$
is determined by __________.

$-a$

$a$

$\left|a\right|$

$\left|b\right|$

$\frac{2\pi}{\left|b\right|}$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The period of either $y=a\sin\left(b\theta\right)\ or\ y=a\cos\left(b\theta\right)$
is determined by __________.

$-a$

$a$

$\left|a\right|$

$\left|b\right|$

$\frac{2\pi}{\left|b\right|}$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

The period of a sine or cosine curve is the horizontal distance that defines one cycle. Periodic graphs such as $y=\sin\left(\theta\right)$ and $y=\cos\left(\theta\right)$ repeat cycles infinitely across the coordinate plane.

True

False

True in some cases, but it depends on the domain and the quadratic coefficient of the asymptotic femur.

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The amplitude of $y=5\sin\left(2\theta\right)$ is ________.

$-5$

$5$

$2\pi$

$\frac{\pi}{2}$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The period of $y=5\sin\left(2\theta\right)$ is ________.

$2$

$\pi$

$2\pi$

$\frac{\pi}{2}$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The graph of $y=5\sin\left(2\theta\right)$ shows the _______________________________________ of $y=\sin\left(\theta\right)$ .

vertical compressing and horizontal stretching

vertical compressing and horizontal compressing

vertical stretching and horizontal stretching

vertical stretching and horizontal compressing

Tags

CCSS.HSF-IF.C.7E

10.

MULTIPLE SELECT QUESTION

3 mins • 1 pt

Check all that apply for the graph of $y=-\frac{1}{4}\cos\left(\frac{2}{5}\theta\right)$ .

Its graph is an x-axis reflection of $y=\cos\left(\theta\right)$

Its graph is a vertical compression of $y=\cos\left(\theta\right)$

Its graph is a horizontal compression of $y=\cos\left(\theta\right)$

its graph has a period of $10\pi$

Its amplitude is $-\frac{1}{4}$

Tags

CCSS.HSF-IF.C.7E

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Graphing Sine and Cosine with amplitude & period changes

The red curve is the graph of ______________.

The blue curve is the graph of ______________.

The amplitude of a sine or cosine wave measures the distance from the midline to the "top" of the wave, which is also the distance from the midline to the "bottom" of the wave.

The amplitude of either y=asin⁡(bθ) or y=acos⁡(bθ)y=a\sin\left(b\theta\right)\ or\ y=a\cos\left(b\theta\right)y=asin(bθ) or y=acos(bθ) is determined by __________.

The period of either y=asin⁡(bθ) or y=acos⁡(bθ)y=a\sin\left(b\theta\right)\ or\ y=a\cos\left(b\theta\right)y=asin(bθ) or y=acos(bθ) is determined by __________.

The period of a sine or cosine curve is the horizontal distance that defines one cycle. Periodic graphs such as y=sin⁡(θ)y=\sin\left(\theta\right)y=sin(θ) and y=cos⁡(θ)y=\cos\left(\theta\right)y=cos(θ) repeat cycles infinitely across the coordinate plane.

The amplitude of y=5sin⁡(2θ)y=5\sin\left(2\theta\right)y=5sin(2θ) is ________.

The period of y=5sin⁡(2θ)y=5\sin\left(2\theta\right)y=5sin(2θ) is ________.

The graph of y=5sin⁡(2θ)y=5\sin\left(2\theta\right)y=5sin(2θ) shows the _______________________________________ of y=sin⁡(θ)y=\sin\left(\theta\right)y=sin(θ) .

Check all that apply for the graph of y=−14cos⁡(25θ)y=-\frac{1}{4}\cos\left(\frac{2}{5}\theta\right)y=−41​cos(52​θ) .

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Discover more resources for Mathematics

The amplitude of either $y=a\sin\left(b\theta\right)\ or\ y=a\cos\left(b\theta\right)$
is determined by __________.

The period of either $y=a\sin\left(b\theta\right)\ or\ y=a\cos\left(b\theta\right)$
is determined by __________.

The period of a sine or cosine curve is the horizontal distance that defines one cycle. Periodic graphs such as $y=\sin\left(\theta\right)$ and $y=\cos\left(\theta\right)$ repeat cycles infinitely across the coordinate plane.

The amplitude of $y=5\sin\left(2\theta\right)$ is ________.

The period of $y=5\sin\left(2\theta\right)$ is ________.

The graph of $y=5\sin\left(2\theta\right)$ shows the _______________________________________ of $y=\sin\left(\theta\right)$ .

Check all that apply for the graph of $y=-\frac{1}{4}\cos\left(\frac{2}{5}\theta\right)$ .