warm up find the ratio for 1. csc(60) 2. sec (30)

Warm up

•Find the ratio for•1. csc(60)

•2. sec (30)

Lesson 5-3 Trig Functions on the Unit Circle Objective: To become familiar with the unit circle, and find the six trig functions on the circle.

Quadrants 90o

180o 360o 2

270o

2

2

3

The Unit Circle•Imagine a circle on

the coordinate plane, with its center at the origin, and a radius of 1.

•Choose a point on the circle somewhere in quadrant I.

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r, 2

00

04

The Unit Circle•Connect the origin to

the point, and from that point drop a perpendicular to the x-axis.

•This creates a right triangle with hypotenuse of 1.

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The Unit Circle – 60o

60o

2

1

1 2

3

( ½, √3 / 2)

The Unit Circle – 60o

-60o or 300o

2

1

1 2

3

( ½, -√3 / 2)

The Unit Circle – 120o

120o

2

1

1 2

3

( -½, √3 / 2)

The Unit Circle – 240o

240o

2

1

1 2

3

( -½, -√3 / 2)

The Unit Circle – 30o

30o

2

1

1

2

3

(√3 / 2, ½)

The Unit Circle – 45o

45o

2

1

1

2

2

( , )

1

1

2

2

√2

2

2

2

2

21

23 ,

21

23 ,

21

23 ,

21

23 ,

(1, 0)

(0, 1)

(-1, 0)

(0, -1)

23

21,

23

21,

23

21,

23

21,

21

21 ,

21

21 ,

21

21 ,

21

21 ,

36020

630

445 3

60

2

90

32120

47315

65150

67210

45225

34240

43135

611330

35300

180

23

270

The Unit Circle

13

All Students Take Calculus• Use the phrase “All Students Take

Calculus” to remember the signs of the trig functions in different quadrants.

AllStudents

Take Calculus

All functions are positive

Sine is positive

Tan is positive

Cos is positive

Online

•unit circle

The Unit Circle

•The Unit Circle can be used to determine what quadrant any point on the circle is. Angleϴ is also referred to as t, the arc of the circle.

•Every point on the circle P(t) = P(x,y) and x and y coordinate on the graph.

Example•Use the unit circle to find each value:•sin(-90o)•cot 270o

Finding Coordinates

• If t = 0 look on the unit circle to see that the point lies on the x axis at (1,0)

•Find t = Find t = -30o

•Find t = π Find t = 300o•Find t = Find t = 270o

2

2

3

Sources

•http://etc.usf.edu/clipart/43200/43215/unit-circle7_43215.htm. 4 Oct 2013

•Pierce, Rod. "Unit Circle" Math Is Fun. Ed. Rod Pierce. 15 Nov 2012. 4 Oct 2013 <http://www.mathsisfun.com/geometry/unit-circle.html>