Given point P (-5, 3) is on the terminal side of angle θ \theta θ , what is sin θ \theta θ ?

3 34 \frac{3}{\sqrt{34}} 3 4 <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"> 3

− 5 34 \frac{-5}{\sqrt{34}} 3 4 <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"> − 5

34 3 \frac{\sqrt{34}}{3} 3 3 4 <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">

Which is the reference angle θ ′ \theta\ ' θ ′ if θ = 11 π 3 \theta=\frac{11\pi}{3} θ = 3 1 1 π ?

12 π 3 \frac{12\pi}{3} 3 1 2 π

tan ⁡ ( − 210 ° ) = ? \tan\left(-210\degree\right)=? tan ( − 2 1 0 ° ) = ?

1 − 3 \frac{1}{-\sqrt{3}} − 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"> 1

− 3 2 \frac{-\sqrt{3}}{2} 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">

cos ⁡ ( 4 π 3 ) = ? \cos\left(\frac{4\pi}{3}\right)=? cos ( 3 4 π ) = ?

− 3 2 \frac{-\sqrt{3}}{2} 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">

− 3 -\sqrt{3} − 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">

Trig Functions of Any Angle

Authored by Douglas Hall

Mathematics

10th - 12th Grade

CCSS covered

Used 80+ times

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10 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the measure of angle a in the triangle above?

$30\degree$

$45\degree$

$60\degree$

$90\degree$

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the measure of angle b in the triangle above?

$30\degree$

$45\degree$

$60\degree$

$90\degree$

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the measure of angle x in the triangle above?

$30\degree$

$45\degree$

$60\degree$

$90\degree$

Tags

CCSS.8.G.B.8

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Given point P (-5, 3) is on the terminal side of angle $\theta$ , what is sin $\theta$ ?

$\frac{3}{\sqrt{34}}$

$\frac{-5}{\sqrt{34}}$

$\frac{-3}{5}$

$\frac{\sqrt{34}}{3}$

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which is the reference angle $\theta\ '$ if $\theta=-135\degree$ ?

$30\degree$

$45\degree$

$60\degree$

$225\degree$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which is the reference angle $\theta\ '$ if $\theta=\frac{11\pi}{3}$ ?

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{12\pi}{3}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\tan\left(-210\degree\right)=?$

$\frac{1}{2}$

$\frac{-\sqrt{3}}{2}$

$\frac{1}{-\sqrt{3}}$

$150\degree$

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\cos\left(\frac{4\pi}{3}\right)=?$

$\frac{-1}{2}$

$\frac{-\sqrt{3}}{2}$

$-\sqrt{3}$

$\frac{\pi}{3}$

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Using the triangle above, $\tan\theta=$ ?

$\frac{4}{5}$

$\frac{3}{5}$

$\frac{4}{3}$

$\frac{3}{4}$

Tags

CCSS.HSG.SRT.C.6

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Trig Functions of Any Angle

What is the measure of angle a in the triangle above?

What is the measure of angle b in the triangle above?

What is the measure of angle x in the triangle above?

Given point P (-5, 3) is on the terminal side of angle θ\thetaθ , what is sin θ\thetaθ ?

Which is the reference angle θ ′\theta\ 'θ ′ if θ=−135°\theta=-135\degreeθ=−135° ?

Which is the reference angle θ ′\theta\ 'θ ′ if θ=11π3\theta=\frac{11\pi}{3}θ=311π​ ?

tan⁡(−210°)=?\tan\left(-210\degree\right)=?tan(−210°)=?

cos⁡(4π3)=?\cos\left(\frac{4\pi}{3}\right)=?cos(34π​)=?

Using the triangle above, tan⁡θ=\tan\theta=tanθ= ?

What is the measure of side x in the triangle above?

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Given point P (-5, 3) is on the terminal side of angle $\theta$ , what is sin $\theta$ ?

Which is the reference angle $\theta\ '$ if $\theta=-135\degree$ ?

Which is the reference angle $\theta\ '$ if $\theta=\frac{11\pi}{3}$ ?

$\tan\left(-210\degree\right)=?$

$\cos\left(\frac{4\pi}{3}\right)=?$

Using the triangle above, $\tan\theta=$ ?