Find sin ⁡ θ \sin\theta sin θ if cot ⁡ θ = 11 60 \cot\theta=\frac{11}{60} cot θ = 6 0 1 1 and π < θ < 3 π 2 \pi<\theta<\frac{3\pi}{2} π < θ < 2 3 π

sin ⁡ θ = − 60 61 \sin\theta=\frac{-60}{61} sin θ = 6 1 − 6 0

sin ⁡ θ = − 3479 60 \sin\theta=-\frac{\sqrt{3479}}{60} sin θ = − 6 0 3 4 7 9 <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">

sin ⁡ θ = − 11 61 \sin\theta=-\frac{11}{61} sin θ = − 6 1 1 1

sin ⁡ θ = − 11 3479 \sin\theta=-\frac{11}{\sqrt{3479}} sin θ = − 3 4 7 9 <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 1

Find cot ⁡ θ \cot\theta cot θ if sin ⁡ θ = 3 5 \sin\theta=\frac{3}{5} sin θ = 5 3 and 0 < θ < π 2 0<\theta<\frac{\pi}{2} 0 < θ < 2 π

cot ⁡ θ = 4 3 \cot\theta=\frac{4}{3} cot θ = 3 4

cot ⁡ θ = 3 4 \cot\theta=\frac{3}{4} cot θ = 4 3

cot ⁡ θ = 4 5 \cot\theta=\frac{4}{5} cot θ = 5 4

cot ⁡ θ = 5 4 \cot\theta=\frac{5}{4} cot θ = 4 5

Find sec ⁡ θ \sec\theta sec θ if sin ⁡ θ = − 1 2 \sin\theta=-\frac{1}{\sqrt{2}} sin θ = − 2 <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 and π < θ < 3 π 2 \pi<\theta<\frac{3\pi}{2} π < θ < 2 3 π

sec ⁡ θ = − 2 \sec\theta=-\sqrt{2} sec θ = − 2 <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">

sec ⁡ θ = − 3 2 \sec\theta=-\frac{\sqrt{3}}{\sqrt{2}} sec θ = − 2 <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 <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">

sec ⁡ θ = 2 3 \sec\theta=\frac{\sqrt{2}}{\sqrt{3}} sec θ = 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"> 2 <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">

sec ⁡ θ = − 1 3 \sec\theta=-\frac{1}{\sqrt{3}} sec θ = − 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

Find cos ⁡ θ \cos\theta cos θ if csc ⁡ θ = 13 5 \csc\theta=\frac{13}{5} csc θ = 5 1 3 and π 2 < θ < π \frac{\pi}{2}<\theta<\pi 2 π < θ < π

cos ⁡ θ = − 12 13 \cos\theta=-\frac{12}{13} cos θ = − 1 3 1 2

cos ⁡ θ = − 194 13 \cos\theta=-\frac{\sqrt{194}}{13} cos θ = − 1 3 1 9 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">

cos ⁡ θ = 13 12 \cos\theta=\frac{13}{12} cos θ = 1 2 1 3

cos ⁡ θ = − 5 194 \cos\theta=\frac{-5}{\sqrt{194}} cos θ = 1 9 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

Find tan ⁡ θ \tan\theta tan θ if cos ⁡ θ = 3 2 \cos\theta=\frac{\sqrt{3}}{2} cos θ = 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"> and 3 π 2 < θ < 2 π \frac{3\pi}{2}<\theta<2\pi 2 3 π < θ < 2 π

tan ⁡ θ = − 1 3 \tan\theta=-\frac{1}{\sqrt{3}} tan θ = − 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

tan ⁡ θ = − 3 \tan\theta=-\sqrt{3} tan θ = − 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">

tan ⁡ θ = − 5 2 \tan\theta=\frac{-\sqrt{5}}{2} tan θ = 2 − 5 <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">

tan ⁡ θ = − 3 5 \tan\theta=-\frac{\sqrt{3}}{\sqrt{5}} tan θ = − 5 <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 <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">

Given tan ⁡ θ = − 15 8 \tan\theta=-\frac{15}{8} tan θ = − 8 1 5 and π 2 < θ < π \frac{\pi}{2}<\theta<\pi 2 π < θ < π , choose those with the correct trig ratio.

csc ⁡ θ = 17 15 \csc\theta=\frac{17}{15} csc θ = 1 5 1 7

sec ⁡ θ = − 17 8 \sec\theta=-\frac{17}{8} sec θ = − 8 1 7

cos ⁡ θ = 15 17 \cos\theta=\frac{15}{17} cos θ = 1 7 1 5

sin ⁡ θ = − 8 17 \sin\theta=-\frac{8}{17} sin θ = − 1 7 8

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Math

Trigonometry

Trigonometric Ratios Sin, Cos, Tan, Csc, Sec And Cot

Finding The Value Of A Trig Ratio Given A Trig Ratio

Finding the Value of a Trig Ratio Given a Trig Ratio

Authored by Cindy Biedrycki

Mathematics

11th - 12th Grade

Used 12+ times

Finding the Value of a Trig Ratio Given a Trig Ratio

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What Quadrant is $\theta$ ? $\frac{3\pi}{2}<\theta<2\pi$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What Quadrant is $\theta$ ? $0<\theta<\frac{\pi}{2}$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What Quadrant is $\theta$ ? $\pi<\theta<\frac{3\pi}{2}$

$\tan\theta=-\sqrt{3}$

$\tan\theta=\frac{-\sqrt{5}}{2}$

$\tan\theta=-\frac{\sqrt{3}}{\sqrt{5}}$

10.

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Given $\tan\theta=-\frac{15}{8}$ and $\frac{\pi}{2}<\theta<\pi$ , choose those with the correct trig ratio.

$\csc\theta=\frac{17}{15}$

$\cos\theta=\frac{15}{17}$

$\sec\theta=-\frac{17}{8}$

$\sin\theta=-\frac{8}{17}$

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Finding the Value of a Trig Ratio Given a Trig Ratio

What Quadrant is θ\thetaθ ? 3π2<θ<2π\frac{3\pi}{2}<\theta<2\pi23π​<θ<2π

What Quadrant is θ\thetaθ ? 0<θ<π20<\theta<\frac{\pi}{2}0<θ<2π​

What Quadrant is θ\thetaθ ? π<θ<3π2\pi<\theta<\frac{3\pi}{2}π<θ<23π​

What Quadrant is θ\thetaθ ? π2<θ<π\frac{\pi}{2}<\theta<\pi2π​<θ<π

Find sin⁡θ\sin\thetasinθ if cot⁡θ=1160\cot\theta=\frac{11}{60}cotθ=6011​ and π<θ<3π2\pi<\theta<\frac{3\pi}{2}π<θ<23π​

Find cot⁡θ\cot\thetacotθ if sin⁡θ=35\sin\theta=\frac{3}{5}sinθ=53​ and 0<θ<π20<\theta<\frac{\pi}{2}0<θ<2π​

Find sec⁡θ\sec\thetasecθ if sin⁡θ=−12\sin\theta=-\frac{1}{\sqrt{2}}sinθ=−2​1​ and π<θ<3π2\pi<\theta<\frac{3\pi}{2}π<θ<23π​

Find cos⁡θ\cos\thetacosθ if csc⁡θ=135\csc\theta=\frac{13}{5}cscθ=513​ and π2<θ<π\frac{\pi}{2}<\theta<\pi2π​<θ<π

Find tan⁡θ\tan\thetatanθ if cos⁡θ=32\cos\theta=\frac{\sqrt{3}}{2}cosθ=23​​ and 3π2<θ<2π\frac{3\pi}{2}<\theta<2\pi23π​<θ<2π

Given tan⁡θ=−158\tan\theta=-\frac{15}{8}tanθ=−815​ and π2<θ<π\frac{\pi}{2}<\theta<\pi2π​<θ<π , choose those with the correct trig ratio.

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