Topics
8. Triangular & Circular Functions
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United States of AmericaUT
Math III

8.04 Trigonometric functions in the coordinate plane

Lesson
Practice

Interactive practice questions

The point on the graph has coordinates $\left(15,8\right)$(15,8).

A Coordinate Plane with x-axis labeled $-30$−30, $-15$−15, $15$15 and $30$30, and y-axis labeled $-16$−16, $-8$−8, $8$8 and $16$16. A point with coordinates $\left(15,8\right)$(15,8) is plotted with a solid black point. A line connects this point to the origin in the Coordinate Plane. The angle between this line and the positive axis is labeled $\theta$θ indicating its unknown measure.
a

Find $r$r, the distance from the point to the origin.

b

Find $\sin\theta$sinθ.

c

Find $\cos\theta$cosθ.

d

Find $\tan\theta$tanθ.

e

Find $\csc\left(\theta\right)$csc(θ).

f

Find $\sec\left(\theta\right)$sec(θ).

g

Find $\cot\left(\theta\right)$cot(θ).

Easy
3min

The point on the graph has coordinates $\left(-7,-24\right)$(−7,−24).

Easy
5min

The point on the graph has coordinates $\left(7,24\right)$(7,24).

Easy
6min

The graph shows an angle $a$a in standard position with its terminal side intersecting the circle at $P$P$\left(\frac{3}{5},\frac{4}{5}\right)$(35​,45​).

Easy
2min
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Outcomes

III.F.TF.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

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