Find the value of sin θ \theta θ given the point ( 2 , − 5 ) \left(2,\ -\sqrt{5}\right) ( 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"> )

− 5 3 -\frac{\sqrt{5}}{3} − 3 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">

− 10 3 -\frac{\sqrt{10}}{3} − 3 1 0 <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 10 10 -\frac{3\sqrt{10}}{10} − 1 0 3 1 0 <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">

10 10 \frac{\sqrt{10}}{10} 1 0 1 0 <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">

Find the values of sinθ , cosθ , and tanθ for the angle θ in standard position having (– 4, –3) on its terminal side.

sin ⁡ θ = − 3 5 , cos ⁡ θ = − 4 5 , tan ⁡ θ = 3 4 \sin\theta=-\frac{3}{5},\ \cos\theta=-\frac{4}{5},\ \tan\theta=\frac{3}{4} sin θ = − 5 3 , cos θ = − 5 4 , tan θ = 4 3

sin ⁡ θ = 4 5 , cos ⁡ θ = − 3 5 , tan ⁡ θ = 4 3 \sin\theta=\frac{4}{5},\ \cos\theta=-\frac{3}{5},\ \tan\theta=\frac{4}{3} sin θ = 5 4 , cos θ = − 5 3 , tan θ = 3 4

sin ⁡ θ = − 3 5 , cos ⁡ θ = 4 5 , tan ⁡ θ = 3 4 \sin\theta=-\frac{3}{5},\ \cos\theta=\frac{4}{5},\ \tan\theta=\frac{3}{4} sin θ = − 5 3 , cos θ = 5 4 , tan θ = 4 3

sin ⁡ θ = 4 5 , cos ⁡ θ = 3 5 , tan ⁡ θ = − 3 4 \sin\theta=\frac{4}{5},\ \cos\theta=\frac{3}{5},\ \tan\theta=-\frac{3}{4} sin θ = 5 4 , cos θ = 5 3 , tan θ = − 4 3

Evaluate: cos ⁡ 3 π 4 \cos\ \frac{3\pi}{4} cos 4 3 π

− 1 2 -\frac{1}{\sqrt{2}} − 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

− 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

2 3 \frac{2}{\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"> 2

2 \sqrt{2} 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">

Trig Functions of any Angle

Authored by Elizabeth Qutob

Mathematics

9th - 12th Grade

CCSS covered

Used 5+ times

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19 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Let (12,-5) be a point on the terminal side of θ.
What is Cos ø?

13/12

12/13

-5/13

-5/12

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Let (3,4) be a point on the terminal side of θ. What is sec ø?

4/3

3/4

5/3

2/3

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

let (-3,-3) be a point on the terminal side of θ.
What is cot θ?

Not me

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the value of sin $\theta$ given the point
$\left(2,\ -\sqrt{5}\right)$

$-\frac{\sqrt{10}}{3}$

$-\frac{3\sqrt{10}}{10}$

$\frac{\sqrt{10}}{10}$

$-\frac{\sqrt{5}}{3}$

Tags

CCSS.HSF.TF.C.8

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

cosθ is positive in

the 1st and 2nd quadrants

the 1st and 3rd quadrants

the 1st and 4th quadrants

the 2nd and 3rd quadrants

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

sinθ is positive in

the 1st and 2nd quadrants

the 1st and 3rd quadrants

the 1st and 4th quadrants

the 2nd and 3rd quadrants

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the reference angle for -30°?

150°

30°

80°

60°

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Trig Functions of any Angle

Let (12,-5) be a point on the terminal side of θ.
What is Cos ø?

Let (3,4) be a point on the terminal side of θ. What is sec ø?

let (-3,-3) be a point on the terminal side of θ.
What is cot θ?