4. Triangular & Circular Functions

4.01 Trigonometric functions as right triangle ratios

4.02 Special right triangles and exact value trigonometric ratios

4.03 Degrees, radians, and angles as rotations

4.04 Trigonometric functions in the coordinate plane

4.05 Trigonometric functions on the unit circle

4.06 Evaluating trigonometric functions: exact values

4.07 Extension: Relating the tangent to the slope of a line

United States of America

Grades 9-12

4.04 Trigonometric functions in the coordinate plane

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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