Suppose that θ \theta θ is in standard position and the given point is on the terminal side of θ \theta θ . Give the exact value of the indicated trig function for θ \theta θ . ( -20, 48); Find sin θ \theta θ

− 5 13 -\frac{5}{13} − 1 3 5

− 12 13 -\frac{12}{13} − 1 3 1 2

Evaluate the equation. cos 90 ° 90\degree 9 0 °

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">

U n d e f i n e d Undefined U n d e f i n e d

Use the reciprocal identity to find the indicated function value. tan ⁡ θ , g i v e n t h a t cot ⁡ θ = 5 4 \tan\theta,\ given\ that\ \cot\theta=\frac{\sqrt{5}}{4} tan θ , g i v e n t h a t cot θ = 4 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">

4 5 5 \frac{4\sqrt{5}}{5} 5 4 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 5 \frac{\sqrt{5}}{5} 5 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">

4 5 \frac{\sqrt{4}}{5} 5 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 5 4 \frac{5\sqrt{5}}{4} 4 5 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">

Find the value of the trigonometric function. Find tan ⁡ θ , \tan\theta, tan θ , given that sin ⁡ θ = 3 4 a n d θ i s i n q u a d r a n t I I . \sin\theta=\frac{3}{4}\ and\ \theta\ is\ in\ quadrant\ II. sin θ = 4 3 a n d θ i s i n q u a d r a n t I I .

− 3 7 7 -\frac{3\sqrt{7}}{7} − 7 3 7 <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">

− 7 9 -\frac{\sqrt{7}}{9} − 9 7 <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 value of the trigonometric function. Find sec ⁡ θ \sec\theta sec θ , given that tan ⁡ θ = 3 4 a n d θ i s i n q u a d r a n t I . \tan\theta=\frac{3}{4}\ and\ \theta\ is\ in\ quadrant\ I. tan θ = 4 3 a n d θ i s i n q u a d r a n t I .

− 7 9 -\frac{\sqrt{7}}{9} − 9 7 <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 7 7 \frac{3\sqrt{7}}{7} 7 3 7 <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 value of the trigonometric function. Find sin ⁡ θ , \sin\theta, sin θ , given that cos ⁡ θ = 4 7 a n d θ i s i n q u a d r a n t I V . \cos\theta=\frac{4}{7}\ and\ \theta\ is\ in\ quadrant\ IV. cos θ = 7 4 a n d θ i s i n q u a d r a n t I V .

− 33 7 -\frac{\sqrt{33}}{7} − 7 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">

− 33 4 -\frac{\sqrt{33}}{4} − 4 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">

− 33 -\sqrt{33} − 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">

5.2 Trigonometric Functions

Mathematics

9th - 12th Grade

CCSS covered

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16 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Sketch an angle $\theta$ in standard position such that $\theta$ has the least positive measure and the point (-2, 5) is on the terminal side of $\theta$ .

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Sketch an angle of $\theta$ in standard position such that $\theta$ has the least positive measure and the given point ( -2,-7) is on the terminal side of
$\theta$ .

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ .

( 6, 8); Find cos $\theta$

$\frac{3}{4}$

$\frac{3}{5}$

$\frac{4}{5}$

$\frac{4}{3}$

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ .
( -3, -2); Find tan $\theta$ .

$\frac{2}{3}$

$\frac{3}{2}$

$-\frac{1}{2}$

$-\frac{3}{4}$

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ .
( -20, 48); Find sin $\theta$

$-\frac{5}{13}$

$-\frac{12}{13}$

$\frac{12}{13}$

$\frac{5}{13}$

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative.
IV, $\frac{x}{y}$

Positive

Negative

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative.
II, $\frac{r}{y}$

Positive

Negative

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative.
III, $\frac{x}{r}$

Positive

Negative

Tags

CCSS.HSF.TF.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Evaluate the equation.
cos $90\degree$

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

$1$

$0$

$Undefined$

Tags

CCSS.HSF.TF.A.2

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Evaluate the expression.
sin $\left(-180\degree\right)$

Undefined

-1

Tags

CCSS.HSF.TF.A.4

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5.2 Trigonometric Functions

Sketch an angle θ\thetaθ in standard position such that \thetaθ has the least positive measure and the point (-2, 5) is on the terminal side of \thetaθ .

Sketch an angle of θ\thetaθ in standard position such that θ\thetaθ has the least positive measure and the given point ( -2,-7) is on the terminal side of θ\thetaθ .

Suppose that θ\thetaθ is in standard position and the given point is on the terminal side of θ\thetaθ . Give the exact value of the indicated trig function for θ\thetaθ .( 6, 8); Find cos θ\thetaθ

Suppose that θ\thetaθ is in standard position and the given point is on the terminal side of θ\thetaθ . Give the exact value of the indicated trig function for θ\thetaθ . ( -3, -2); Find tan θ\thetaθ .

Suppose that θ\thetaθ is in standard position and the given point is on the terminal side of θ\thetaθ . Give the exact value of the indicated trig function for θ\thetaθ . ( -20, 48); Find sin θ\thetaθ

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative. IV, xy\frac{x}{y}yx​

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative. II, ry\frac{r}{y}yr​

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative. III, xr\frac{x}{r}rx​

Evaluate the equation.cos 90°90\degree90°

Evaluate the expression.sin (−180°)\left(-180\degree\right)(−180°)

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Sketch an angle $\theta$ in standard position such that $\theta$ has the least positive measure and the point (-2, 5) is on the terminal side of $\theta$ .

Sketch an angle of $\theta$ in standard position such that $\theta$ has the least positive measure and the given point ( -2,-7) is on the terminal side of
$\theta$ .

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ .

( 6, 8); Find cos $\theta$

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ .
( -3, -2); Find tan $\theta$ .

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ .
( -20, 48); Find sin $\theta$

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative.
IV, $\frac{x}{y}$

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative.
II, $\frac{r}{y}$

If r is a positive number and the point (x,y) is in the indicated quadrant, decide whether the given ratio is positive or negative.
III, $\frac{x}{r}$

Evaluate the equation.
cos $90\degree$

Evaluate the expression.
sin $\left(-180\degree\right)$