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 90 o 180 o 360 o o

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. ©Carolyn C. Wheater,

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. ©Carolyn C. Wheater,

The Unit Circle – 60 o 60 o 1 ( ½, √3 / 2)

The Unit Circle – 60 o -60 o or 300 o 1 ( ½, -√3 / 2)

The Unit Circle – 120 o 120 o 1 ( -½, √3 / 2)

The Unit Circle – 240 o 240 o 1 ( -½, -√3 / 2)

The Unit Circle – 30 o 30 o 1 (√3 / 2, ½)

The Unit Circle – 45 o 45 o 1 (, ) 1 1 √2

(1, 0) (0, 1) (-1, 0) (0, -1) 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. All Students TakeCalculus 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. Angle 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(-90 o ) cot 270 o

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 = -30 o Find t = π Find t = 300 o Find t = Find t = 270 o

Sources circle7_43215.htm. 4 Oct 2013http://etc.usf.edu/clipart/43200/43215/unit- circle7_43215.htm Pierce, Rod. "Unit Circle" Math Is Fun. Ed. Rod Pierce. 15 Nov Oct 2013