Precalculus Radians and the Unit Circle Worksheet (PDF)

Precalculus math worksheet: Radians and the Unit Circle – Maths PDF

Cover of the book Precalculus Math Worksheets with Answers (PDF)

Download as a PDFThe Precalculus worksheets book with answersPrintable PDFSee the book ›

Sommaire

This angles unit circle worksheet for Precalculus covers radians and the unit circle (Common Core F-TF.A.1, F-TF.A.2, F-TF.A.3, F-TF.A.4), with a free PDF to print.

These 20 problems practice radians and the unit circle (Common Core F-TF.A.1 through F-TF.A.4). You will convert angles, find arc length and sector area, use reference angles and evaluate exact trigonometric values.

Precalculus · Common Core State Standards: F-TF.A.1, F-TF.A.2, F-TF.A.3, F-TF.A.4

Angles unit circle worksheet: exercises 1 to 10

Exercise 1 – Degrees to radians

Convert \(45^{\circ}\) and \(150^{\circ}\) to radians.

Exercise 2 – Radians to degrees

Convert \(\frac{\pi}{6}\) and \(\frac{5\pi}{4}\) to degrees.

Exercise 3 – Calculator conversion

Convert \(3\) radians to degrees and \(100^{\circ}\) to radians, to the nearest hundredth.

Exercise 4 – Coterminal angles

Find one positive and one negative angle coterminal with \(50^{\circ}\), and one of each for \(\frac{7\pi}{4}\) (measured in radians, using the next turn).

Exercise 5 – Reference angle

Find the reference angle for \(150^{\circ}\) and for \(\frac{5\pi}{4}\).

Exercise 6 – Quadrants

Three angles on the unit circle.

Name the quadrant of the terminal side of \(200^{\circ}\), \(-45^{\circ}\) and \(\frac{11\pi}{6}\).

Exercise 7 – Arc length

Sector of a circle.

Find the arc length on a circle of radius \(6\) inches for a central angle of \(\frac{\pi}{3}\).

Exercise 8 – Sector area

Find the area of a sector with radius \(10\) ft and central angle \(\frac{2\pi}{5}\).

Exercise 9 – Find the angle

An arc of \(15\) ft is cut off on a circle of radius \(6\) ft. Find the central angle in radians and in degrees (nearest tenth).

Exercise 10 – Exact values, first quadrant

Evaluate \(\sin30^{\circ}\), \(\cos45^{\circ}\) and \(\tan60^{\circ}\).

Exercises 11 and up

Exercise 11 – Exact values, other quadrants

Evaluate \(\cos\frac{2\pi}{3}\), \(\sin\frac{5\pi}{4}\) and \(\tan\frac{3\pi}{4}\).

Exercise 12 – Point on the unit circle

Angle 5pi/6 on the unit circle.

The terminal side of \(\theta=\frac{5\pi}{6}\) meets the unit circle at a point. Find its coordinates and \(\tan\theta\).

Exercise 13 – Find the other values

If \(\sin\theta=\frac35\) and \(\theta\) is in quadrant II, find \(\cos\theta\) and \(\tan\theta\).

Exercise 14 – Another quadrant

If \(\cos\theta=-\frac{5}{13}\) and \(\theta\) is in quadrant III, find \(\sin\theta\) and \(\tan\theta\).

Exercise 15 – Negative angles

Evaluate \(\sin\left(-\frac{\pi}{6}\right)\) and \(\cos\left(-\frac{\pi}{3}\right)\).

Exercise 16 – Large and negative angles

Evaluate \(\sin\frac{7\pi}{3}\) and \(\cos\left(-\frac{5\pi}{6}\right)\).

Exercise 17 – Ferris wheel

Ferris wheel of radius 25 feet.

A Ferris wheel of radius \(25\) ft turns \(3\) revolutions per minute. Find its angular speed in radians per second, and the distance a rider travels in \(10\) seconds.

Exercise 18 – Pizza slice

One slice of a 14-inch pizza.

A \(14\)-inch pizza is cut into \(8\) equal slices. Find the crust length and area of one slice, to the nearest hundredth.

Exercise 19 – Windshield wiper

A wiper blade arm sweeps through \(120^{\circ}\). The blade reaches \(18\) inches from the pivot. Find the area of the swept sector.

Exercise 20 – Distance on Earth

Two cities lie on the same meridian, \(5^{\circ}\) of latitude apart. Using Earth’s radius of \(3{,}959\) miles, find the distance between them to the nearest mile.

Key facts behind this angles unit circle worksheet

Key facts

pi radians = 180 degrees; convert with the factor pi/180 or 180/pi.
Arc length s = r theta and sector area A = (1/2) r^2 theta, with theta in radians.
The point on the unit circle at angle theta is (cos theta, sin theta).
Reference angle: the acute angle to the x-axis; the quadrant sets the sign.
Coterminal angles differ by 2 pi and have the same trig values.

How to use this angles unit circle worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the angles unit circle worksheet as a PDF with the button below and keep it with your notes.

All Precalculus chapters: Precalculus math.

Voter.. post

Free printable PDF