Thinking about angles and quadrants Special Triangles Graphing Write and scratch Practice 1What goes with what, I forgot. Rectangles Practice 2 Here are.

Slides:



Advertisements
Similar presentations
By bithun jith maths project.
Advertisements

Trigonometric Functions
Special Angles and their Trig Functions
THE UNIT CIRCLE 6.1 Let’s take notes and fill out the Blank Unit Circle as we go along.
Trigonometric Functions
Sum and Difference Identities for Sine and Tangent
13-3 The Unit Circle Warm Up Lesson Presentation Lesson Quiz
13-2 (Part 1): 45˚- 45 ˚- 90˚ Triangles
13.2 – Angles and the Unit Circle
Trigonometric Ratios in the Unit Circle. Warm-up (2 m) 1. Sketch the following radian measures:
Review
Review of Trigonometry
Using Polar Coordinates Graphing and converting polar and rectangular coordinates.
Quiz Find a positive and negative co-terminal angle with: co-terminal angle with: 2.Find a positive and negative co-terminal angle with: co-terminal.
Vocabulary: Initial side & terminal side: Terminal side Terminal side
Signs of functions in each quadrant. Page 4 III III IV To determine sign (pos or neg), just pick angle in quadrant and determine sign. Now do Quadrants.
March 2 nd copyright2009merrydavidson HAPPY BIRTHDAY TO: Khalil Nanji.
7-4 Evaluating Trigonometric Functions of Any Angle Evaluate trigonometric functions of any angle Use reference angles to evaluate trigonometric functions.
Angles and Arcs in the Unit Circle Radian and Degree Measure In this section, we will study the following topics: Terminology used to describe.
Copyright © Cengage Learning. All rights reserved.
CalculusDay 1 Recall from last year  one full rotation = Which we now also know = 2π radians Because of this little fact  we can obtain a lot of.
Introduction The six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) can be used to find the length of the sides of a.
UNIT CIRCLE. Review: Unit Circle – a circle drawn around the origin, with radius 1.
Finding Exact Values For Trigonometry Functions (Then Using those Values to Evaluate Trigonometry functions and Solve Trigonometry Equations)
6.4 Trigonometric Functions
1 Trigonometric Functions of Any Angle & Polar Coordinates Sections 8.1, 8.2, 8.3,
7.5 The Other Trigonometric Functions
Trigonometry functions of A General Angle
– Angles and the Unit Circle
Unit 8 Trigonometric Functions Radian and degree measure Unit Circle Right Triangles Trigonometric functions Graphs of sine and cosine Graphs of other.
Graphing (Method for sin\cos, cos example given) Graphing (Method for cot) Graphing (sec\csc, use previous cos graph from example above) Tangent Graphing,
Copyright © Cengage Learning. All rights reserved. Analytic Trigonometry.
Trigonometric Equations M 140 Precalculus V. J. Motto.
7-5 The Other Trigonometric Functions Objective: To find values of the tangent, cotangent, secant, and cosecant functions and to sketch the functions’
Our goal in todays lesson will be to build the parts of this unit circle. You will then want to get it memorized because you will use many facts from.
Warm Up 1)Find an angle between 0° and 360° that is coterminal with 1190°. 2)Convert 45 degrees to radians.
MATH 31 LESSONS Chapters 6 & 7: Trigonometry
WHAT ARE SPECIAL RIGHT TRIANGLES? HOW DO I FIND VALUES FOR SIN, COS, TAN ON THE UNIT CIRCLE WITHOUT USING MY CALCULATOR? Exact Values for Sin, Cos, and.
Amplitude, Period, and Phase Shift
Section 4.5 Graphs of Sine and Cosine. Overview In this section we first graph y = sin x and y = cos x. Then we graph transformations of sin x and cos.
Section 7-4 Evaluating and Graphing Sine and Cosine.
The Unit Circle M 140 Precalculus V. J. Motto. Remembering the “special” right triangles from geometry. The first one is formed by drawing the diagonal.
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.
Trigonometric Functions: The Unit Circle Section 4.2.
+. + Bellwork + Objectives You will be able to use reference angles to evaluate the trig functions for any angle. You will be able to locate points on.
Jeopardy Dividing Poly’s Polynomials Rationals! Unit.
Warm Up Find the exact value of each trigonometric function. 1. sin 60°2. tan 45° 3. cos 45° 4. cos 60° 1 EQ: How can I convert between degrees and radians?
Chapter 4 Review of the Trigonometric Functions
1.6 Trigonometric Functions: The Unit circle
Chapter 5 Verifying Trigonometric Identities
Graphing Sine and Cosine Amplitude Horizontal & Vertical Shifts Period Length.
Periodic Function Review
The Fundamental Identity and Reference Angles. Now to discover my favorite trig identity, let's start with a right triangle and the Pythagorean Theorem.
Gettin’ Triggy wit it H4Zo.
Do Now: given the equation of a circle x 2 + y 2 = 1. Write the center and radius. Aim: What is the unit circle? HW: p.366 # 4,6,8,10,18,20 p.367 # 2,4,6,8.
Notes 10.7 – Polar Coordinates Rectangular Grid (Cartesian Coordinates) Polar Grid (Polar Coordinates) Origin Pole Positive X-axis Polar axis There is.
Jeopardy!. Categories Coterminal Angles Radians/ Degrees Unit CircleQuadrants Triangle Trig Angle of elevation and depression $100 $200 $300 $400.
WARM UP Write the general equation of an exponential function. Name these Greek letters β, θ, Δ, ε What transformation of the pre-image function y = x.
Trigonometric Functions: The Unit Circle  Identify a unit circle and describe its relationship to real numbers.  Evaluate trigonometric functions.
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle Common Core Standards for Chapter 6 The arc in.
Unit 7: Trigonometric Functions Graphing the Trigonometric Function.
Entry Task Complete the vocabulary
Unit 3 Trigonometry Review Radian Measure Special Angles Unit Circle 1.
The Trigonometric Functions. hypotenuse First let’s look at the three basic trigonometric functions SINE COSINE TANGENT They are abbreviated using their.
WARM UP By composite argument properties cos (x – y) =
Addition and Subtraction Formulas
Solving for Exact Trigonometric Values Using the Unit Circle
THE UNIT CIRCLE.
Objectives Students will learn how to use special right triangles to find the radian and degrees.
Solving for Exact Trigonometric Values Using the Unit Circle
Presentation transcript:

Thinking about angles and quadrants Special Triangles Graphing Write and scratch Practice 1What goes with what, I forgot. Rectangles Practice 2 Here are some various memorization techniques. These may or may not be the best for you, but you can look through it and see if it helps or not. Perhaps a combination of methods may help. Please mistakes or suggestions to

First things first. You must know radians as well as you know degrees. Radians are your favorites. A quick way to work out the co-terminal angles without fumbling around too much is to just double the denominator. That is a quick way to find the equivalent of 2π. 3 times 2 6 times 2 Having trouble figuring out what quadrant everything goes in? Here is one method: Eh, it’s not the greatest, but it’s an option. You could try working common denominators. I II III IV But nothing beats familiarity, so study your unit circle. You should be able to spot quadrants with radians as quickly as you would with degrees!!!!

Big  Small: Divide Small  Big: Multiply Remember, radius of unit circle is 1. Radians Degrees 1 1 1

Cos, sin goes with what? Darn, what’s the first coordinate? Positive or Negative? Radians, Degrees Conversion? If you forget, just remember cos is before sin alphabetically. So cos relates to x in the unit circle, and sin with y on the unit circle. In the first triangle, it’s longer on the bottom than it is tall. You can go with ASTC S A T C Or common sense it with cos  x, sin  y, and look to see if x and y are positive or negative. Unless this clicks, ASTC might be easier. Just remember that π = 180 o, and put everything in the right place, π with radians, 180 o with degrees.

A) Factor out the coefficient of x, and use even-odd properties to simplify 1)Find Amplitude and period 2)Find Phase Shift, and vertical shift 3)Find starting and ending x-coordinates 4)Divide into 4 equal parts 5)Label key points 6) Connect Remember, cos(x) = cos(-x) You will always do this, this is part of your ‘work’ on a test and is required Amplitude = T = P.S. = V.S. = Starting point is phase shift. Ending point is Phase shift + Period You will take the starting and ending points and find the average, then find the average again to break it up into four equal regions You want to study the sine and cosine graphs. Remember: Sine  0, 1, 0, -1, 0 Cosine  1, 0, -1, 0, 1 You are basically performing transformations on those key points 1

1) Start with a quick sketch of the first quadrant, unit circle values, and radian denominators. 2) Identify denominator of the problem. 3) Locate quadrant. 4) Follow rectangle, attach correct sign, use x for cosine, y for sine S A T C Try these problems (next click will bring up all solutions) The rectangles will hopefully become unnecessary as you work through these problems more and more. There are many variations of this method that are just as useful.

A) Make sure all values are reduced 1) Start with unit circle values next to denominators. Also, ASTC diagram. S A T C 2) Write down all the coordinates based on the denominator. 3) Cross out values you don’t want. Keep x for cosine, y for sine. 4) Figure out the quadrant, attach sign. Positive Negative Key is to be quick with your quadrants, and keep things neat and watch out for signs.

STOP When you click, the problems will appear. After 150 seconds (2.5 minutes), the word stop will appear. The next click will bring up the answers (hopefully they are correct =^- )

STOP When you click, the problems will appear. After 210 seconds (3.5 minutes), the word stop will appear. The next click will bring up the answers (hopefully they are correct =^- )