Suppose cos ⁡ θ = x θ \cos\theta=x_{\theta}\ \ cos θ = x θ and sin ⁡ θ = y θ \sin\theta=y_{\theta} sin θ = y θ find the values of cos ⁡ ( π − θ ) \cos\left(\pi-\theta\right) cos ( π − θ ) and sin ⁡ ( π − θ ) \sin\ \left(\pi-\theta\right) sin ( π − θ )

( − x θ , y θ ) \left(-x_{\theta},\ y_{\theta}\right) ( − x θ , y θ )

( x θ , y θ ) \left(x_{\theta},\ y_{\theta}\right) ( x θ , y θ )

( x θ , − y θ ) \left(x_{\theta},\ -y_{\theta}\right) ( x θ , − y θ )

( − x θ , − y θ ) \left(-x_{\theta},\ -y_{\theta}\right) ( − x θ , − y θ )

Suppose cos ⁡ θ = x θ \cos\theta=x_{\theta}\ \ cos θ = x θ and sin ⁡ θ = y θ \sin\theta=y_{\theta} sin θ = y θ find the values of cos ⁡ ( π + θ ) \cos\left(\pi+\theta\right) cos ( π + θ ) and sin ⁡ ( π + θ ) \sin\ \left(\pi+\theta\right) sin ( π + θ )

( − x θ , − y θ ) \left(-x_{\theta},\ -y_{\theta}\right) ( − x θ , − y θ )

( x θ , y θ ) \left(x_{\theta},\ y_{\theta}\right) ( x θ , y θ )

( − x θ , y θ ) \left(-x_{\theta},\ y_{\theta}\right) ( − x θ , y θ )

( x θ , − y θ ) \left(x_{\theta},\ -y_{\theta}\right) ( x θ , − y θ )

Suppose cos ⁡ θ = x θ \cos\theta=x_{\theta}\ \ cos θ = x θ and sin ⁡ θ = y θ \sin\theta=y_{\theta} sin θ = y θ find the values of cos ⁡ ( − θ ) \cos\left(-\theta\right) cos ( − θ ) and sin ⁡ ( − θ ) \sin\ \left(-\theta\right) sin ( − θ )

( x θ , − y θ ) \left(x_{\theta},\ -y_{\theta}\right) ( x θ , − y θ )

( x θ , y θ ) \left(x_{\theta},\ y_{\theta}\right) ( x θ , y θ )

( − x θ , y θ ) \left(-x_{\theta},\ y_{\theta}\right) ( − x θ , y θ )

( − x θ , − y θ ) \left(-x_{\theta},\ -y_{\theta}\right) ( − x θ , − y θ )

cos ⁡ θ = 0.87 \cos\theta=0.87\ cos θ = 0 . 8 7 and sin ⁡ θ = 0.50 \sin\theta=0.50 sin θ = 0 . 5 0 find the values of cos ⁡ ( π − θ ) \cos\left(\pi-\theta\right) cos ( π − θ ) and sin ⁡ ( π − θ ) \sin\left(\pi-\theta\right) sin ( π − θ )

( − 0.87 , 0.50 ) \left(-0.87,\ 0.50\right) ( − 0 . 8 7 , 0 . 5 0 )

( 0.87 , 0.50 ) \left(0.87,0.50\right) ( 0 . 8 7 , 0 . 5 0 )

( 0.87 , − 0.50 ) \left(0.87,\ -0.50\right) ( 0 . 8 7 , − 0 . 5 0 )

( − 0.87 , − 0.50 ) \left(-0.87,-0.50\right) ( − 0 . 8 7 , − 0 . 5 0 )

Based on the diagram select all the statements that are true

The coordinates of P' are (x,-y)

The value of sin ⁡ ( − θ ) \sin\ \left(-\theta\right) sin ( − θ ) is equal to the opposite value of sin ⁡ ( θ ) \sin\left(\theta\right) sin ( θ )

The coordinates of P' are (-x, y)

The value of sin ⁡ ( − θ ) \sin\left(-\theta\right)\ sin ( − θ ) is equal to the value of sin ⁡ ( θ ) \sin\ \left(\theta\right) sin ( θ )

Based on the diagram select all the statements that are true

The coordinates of P' are (x,-y)

The value of cos ⁡ ( − θ ) \cos\left(-\theta\right)\ cos ( − θ ) is equal to the value of cos ⁡ ( θ ) \cos\ \left(\theta\right) cos ( θ )

The coordinates of P' are (-x, y)

The value of cos ⁡ ( − θ ) \cos\ \left(-\theta\right) cos ( − θ ) is equal to the opposite value of cos ⁡ ( θ ) \cos\left(\theta\right) cos ( θ )

Based on the diagram select the statement that is true

The coordinates of P' are ( − cos ⁡ θ , − sin ⁡ θ ) \left(-\cos\theta,-\sin\theta\right) ( − cos θ , − sin θ )

The coordinates of P' are ( cos ⁡ θ , − sin ⁡ θ ) \left(\cos\theta,-\sin\theta\right) ( cos θ , − sin θ )

The coordinate of P' are ( − cos ⁡ θ , sin ⁡ θ ) \left(-\cos\theta,\ \sin\theta\right) ( − cos θ , sin θ )

Based on the diagram select all the true statements

\sin\left(-\theta\right)\ sin ( − θ ) is the opposite value as the \sin\left(\theta\right) sin ( θ )

cos ⁡ ( − θ ) \cos\left(-\theta\right) cos ( − θ ) is the same value as the cos ⁡ ( θ ) \cos\left(\theta\right) cos ( θ )

sin ⁡ ( − θ ) \sin\left(-\theta\right)\ sin ( − θ ) is the same value as the sin ⁡ ( θ ) \sin\left(\theta\right) sin ( θ )

\cos\left(-\theta\right) cos ( − θ ) is the opposite value as the \cos\left(\theta\right) cos ( θ )

Find the missing values for A, B and C

A = 1 2 , B = − 1 2 , a n d C = − 1 2 A=\frac{1}{2},\ B=-\frac{1}{2},\ and\ \ C=-\frac{1}{2} A = 2 1 , B = − 2 1 , a n d C = − 2 1

A = 1 2 , B = 1 2 , a n d C = − 1 2 A=\frac{1}{2},\ B=\frac{1}{2},\ and\ \ C=-\frac{1}{2} A = 2 1 , B = 2 1 , a n d C = − 2 1

A = − 1 2 , B = 1 2 , a n d C = − 1 2 A=-\frac{1}{2},\ B=\frac{1}{2},\ and\ \ C=-\frac{1}{2} A = − 2 1 , B = 2 1 , a n d C = − 2 1

A = 1 2 , B = − 1 2 , a n d C = 1 2 A=\frac{1}{2},\ B=-\frac{1}{2},\ and\ \ C=\frac{1}{2} A = 2 1 , B = − 2 1 , a n d C = 2 1

Find the missing values for A, B and C

A = − 3 2 , B = − 3 2 , a n d C = 3 2 A=-\frac{\sqrt{3}}{2},\ B=-\frac{\sqrt{3}}{2},\ and\ \ \ C=\frac{\sqrt{3}}{2} A = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , B = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , a n d C = 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

A = 3 2 , B = 3 2 , a n d C = − 3 2 A=\frac{\sqrt{3}}{2},\ B=\frac{\sqrt{3}}{2},\ and\ \ C=-\frac{\sqrt{3}}{2} A = 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , B = 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , a n d C = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

A = − 3 2 , B = 3 2 , a n d C = − 3 2 A=-\frac{\sqrt{3}}{2},\ B=\frac{\sqrt{3}}{2},\ and\ \ C=-\frac{\sqrt{3}}{2} A = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , B = 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , a n d C = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

A = 3 2 , B = − 3 2 , a n d C = − 3 2 A=\frac{\sqrt{3}}{2},\ B=-\frac{\sqrt{3}}{2},\ and\ \ \ C=-\frac{\sqrt{3}}{2} A = 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , B = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , a n d C = − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

What statement describes your horizontal position with respect to the vertical center line as the Ferris Wheel rotates CCW through QI

My position moves towards the center line and my distance from the center line decreases

My position moves towards the center line and my distance from the center line increases

My position moves away from the center line and my distance from the center line increases

My position moves away from the center line and my distance from the center line decreases

Unit Circle Symmetry Reloaded

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Mathematics

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9th - 12th Grade

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Practice Problem

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Medium

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CCSS

HSF.TF.A.4, HSF.TF.C.9, HSF.TF.A.2

Standards-aligned

Don Krolak

Used 50+ times

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CCSS.HSF.TF.C.9

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Suppose cos⁡θ=xθ \cos\theta=x_{\theta}\ \ cosθ=xθ​ and sin⁡θ=yθ\sin\theta=y_{\theta}sinθ=yθ​ find the values of cos⁡(π−θ)\cos\left(\pi-\theta\right)cos(π−θ) and sin⁡ (π−θ)\sin\ \left(\pi-\theta\right)sin (π−θ)

Suppose cos⁡θ=xθ \cos\theta=x_{\theta}\ \ cosθ=xθ​ and sin⁡θ=yθ\sin\theta=y_{\theta}sinθ=yθ​ find the values of cos⁡(π+θ)\cos\left(\pi+\theta\right)cos(π+θ) and sin⁡ (π+θ)\sin\ \left(\pi+\theta\right)sin (π+θ)

Suppose cos⁡θ=xθ \cos\theta=x_{\theta}\ \ cosθ=xθ​ and sin⁡θ=yθ\sin\theta=y_{\theta}sinθ=yθ​ find the values of cos⁡(−θ)\cos\left(-\theta\right)cos(−θ) and sin⁡ (−θ)\sin\ \left(-\theta\right)sin (−θ)

Which rotation results in flipping the point on the unit circle over the x axis.

Which rotation results in flipping the point on the unit circle over the y axis.

Which rotation results in flipping the point on the unit circle over the origin

cos⁡θ=0.87 \cos\theta=0.87\ cosθ=0.87 and sin⁡θ=0.50\sin\theta=0.50sinθ=0.50 find the values of cos⁡(π−θ)\cos\left(\pi-\theta\right)cos(π−θ) and sin⁡(π−θ)\sin\left(\pi-\theta\right)sin(π−θ)

Based on the diagram select all the statements that are true

Based on the diagram select all the statements that are true

Based on the diagram select the statement that is true

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Suppose $\cos\theta=x_{\theta}\ \$ and $\sin\theta=y_{\theta}$ find the values of $\cos\left(\pi-\theta\right)$ and $\sin\ \left(\pi-\theta\right)$

Suppose $\cos\theta=x_{\theta}\ \$ and $\sin\theta=y_{\theta}$ find the values of $\cos\left(\pi+\theta\right)$ and $\sin\ \left(\pi+\theta\right)$

Suppose $\cos\theta=x_{\theta}\ \$ and $\sin\theta=y_{\theta}$ find the values of $\cos\left(-\theta\right)$ and $\sin\ \left(-\theta\right)$

$\cos\theta=0.87\$ and $\sin\theta=0.50$ find the values of $\cos\left(\pi-\theta\right)$ and $\sin\left(\pi-\theta\right)$