warm up find the ratio for 1. csc(60) 2. sec (30)
TRANSCRIPT
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.
©C
aro
lyn
C. W
heate
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.
©C
aro
lyn
C. W
heate
r, 2
00
05
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
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>