A circle with center at (0, 0) and radius 1 is called a unit circle.

Slides:



Advertisements
Similar presentations
Find the period of the function y = 4 sin x
Advertisements

Warm-Up Find the following. 1.) sin 30 ◦ 2.) cos 270 ◦ 3.) cos 135 ◦
30º 60º 1 45º 1 30º 60º 1 Do Now: Find the lengths of the legs of each triangle.
_______º _______ rad _______º ________ rad ­­­­ _______º _______ rad _______º _______ rad ­­­­ _______º _______ rad ______º _______ rad Unit Circle use.
Section 6.1 Notes Special Angles of the Unit Circle in degrees and radians.
5.3 The Unit Circle. A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be So points on this circle.
Trigonometry Exact Value Memory Quiz A Trigonometry Exact Value Memory Quiz A.
9.6 Circles in the Coordinate Plane Date: ____________.
Unit Circle ( √3, 1 ) 2 2 ( 1, √3 ) 2 2 ( √2, √2 ) ˚ 45˚ 60˚
EQ: How do you convert from degrees to radians and from radians to degrees? Demonstrated in writing in performance task (Unit 5 Task 2). WARM UP Create.
Objective: Use unit circle to define trigonometric functions. Even and odd trig functions. Warm up 1.Find and. 2.Give the center and radius of a circle.
Unit Circle. Special Triangles Short Long Hypotenuse s s 2s Hypotenuse 45.
9.3 - Circles Objectives: Write an equation for a circle given sufficient information. Given an equation of a circle, graph it and label the radius and.
Equations of Circles.
Circles in the Coordinate Plane
C2 TRIGONOMETRY.
GRADE 12 PRE-CALCULUS CIRCLES & Radian Measure
Trigonometry Review.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Polar Coordinates r   Pole Polar axis.
Examples: Intro to Conics - Circles
Equations of Circles.
Pre-Calc: 4.2: Trig functions: The unit circle
Do Now Find the value of each expression. Sin 60 ° Cos 30 ° Tan 270 °
UNIT CIRCLE THE.
4.2 Trigonometric Function: The Unit circle
Bell Ringer How many degrees is a radian?
Notes Over 10.3 r is the radius radius is 4 units
10.6 Equations of Circles Geometry.
Additional Topics in math Lessons 5-7
Trigonometric Function: The Unit circle
Unit 8 The Unit Circle!.
Warmup Find sin , cos , and tan .
Appendix D: Trigonometry
Circumscribed Circles
REVIEW for QUIZ Grade 12.
Unit Circle 1 (0,0) Center: Radius: -1.
2. The Unit circle.
Section 3 – Trig Functions on the Unit Circle
What is a radius of a circle? What about the diameter?
Trigonometric Equations with Multiple Angles
LESSON ____ SECTION 4.2 The Unit Circle.
Equations of Circles.
1 step solns A Home End 1) Solve Sin x = 0.24
Trigonometric Function: The Unit circle
47.75⁰ Convert to radians: 230⁰.
6.1 Angles and Radian Measure
THE UNIT CIRCLE.
Unit 7B Review.
How do we convert angle measures between degrees and radians?
4.1 Equations of circles Arcs, Inscribed Angles, Central Angles
4.2 Trigonometric Function: The Unit circle
Objectives Students will learn how to use special right triangles to find the radian and degrees.
Trigonometric Functions:
Principal Values of the Inverse Trig Functions
5.2 Trigonometric Functions: Unit Circle Approach
Trigonometric Functions: Unit Circle Approach
Trig. Ratios in a Coordinate System
trigonometry Radian measure
( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )
EQ: Are there other ways to describe the location of a point in the plane other than by giving its x- and y- coordinates?
Conversions, Angle Measures, Reference, Coterminal, Exact Values
Circles in the Coordinate Plane
Day 49 Agenda: DG minutes.
5.2 Trigonometric Functions: Unit Circle Approach
Graphing Polar Coordinates
Academy Algebra II THE UNIT CIRCLE.
5-3 The Unit Circle.
Chapter Equations of Circles.
Given A unit circle with radius = 1, center point at (0,0)
Presentation transcript:

A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be (0,1) (-1,0) (1,0) (0,-1) So points on this circle must satisfy this equation.

Label the 4 principal angles that lie on the x and y axes of the unit circle in degrees. Label the special angles around the unit circle in degrees. Label the 4 principal angles that lie on the x and y axes in radians. Label each angle that is a multiple of 60˚ in radians Label each angle that is a multiple of 45 ˚ in radians Label the remaining special angles in radians. Write the coordinates (x, y) for the points on the unit circle that lie on the x and y axes. Write the coordinates (x, y) for all of the angles whose reference angles are 45˚ (π/4 radians). Write the coordinates (x, y) for all of the angles whose reference angles are 30˚ (π/6 radians). Write the coordinates (x, y) for all of the angles whose reference angles are 60˚ (π/3 radians).

Complete. Angle (rad) sin cos tan π/2 π 3π/2 Angle (rad) sin cos tan π/2 π 3π/2 Angle (rad) sin cos tan π/6 5π/6 7π/6 11π/6 Angle (rad) sin cos tan π/4 3π/4 5π/4 7π/4 Angle (rad) sin cos tan π/3 2π/3 4π/3 5π/3