Trigonometric functions The relationship between trigonometric functions and a unit circle A.V.Ali www.2july-maths.co.uk.

Slides:



Advertisements
Similar presentations
GRAPHS OF OTHER TRIG FUNCTIONS
Advertisements

1.4 Reference Angles.
Trigonometric Identities
Graphs of other Trig Functions Section 4.6. Cosecant Curve What is the cosecant x? Where is cosecant not defined? ◦Any place that the Sin x = 0 The curve.
Lesson 2: Trigonometric Ratios of Complementary Angles Trigonometric Co-functions Prepared By: Nathan Ang (19) Ivan Yeo (13) Nicholas Tey (22) Yeo Kee.
The Inverse Trigonometric Functions Section 4.2. Objectives Find the exact value of expressions involving the inverse sine, cosine, and tangent functions.
Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x Select the correct answer:
Section 5.3 Trigonometric Functions on the Unit Circle
7.3 Trigonometric Functions of Angles. Angle in Standard Position Distance r from ( x, y ) to origin always (+) r ( x, y ) x y  y x.
Section 7.2 The Inverse Trigonometric Functions (Continued)
Pre calculus Problem of the Day Homework: p odds, odds, odds On the unit circle name all indicated angles by their first positive.
5.2-The Unit Circle & Trigonometry. 1 The Unit Circle 45 o 225 o 135 o 315 o 30 o 150 o 110 o 330 o π6π6 11π 6 5π65π6 7π67π6 7π47π4 π4π4 5π45π4 3π43π4.
4.2, 4.4 – The Unit Circle, Trig Functions The unit circle is defined by the equation x 2 + y 2 = 1. It has its center at the origin and radius 1. (0,
Section 4.6 Graphs of Other Trigonometric Functions.
Unit Circle Approach Properties of the Trigonometric Functions Section 5.
Section 5.3 Trigonometric Functions on the Unit Circle
4.6 Graphs of Other Trigonometric Functions Objectives –Understand the graph of y = tan x –Graph variations of y = tan x –Understand the graph of y = cot.
Chapter 4 Trigonometric Functions
Aim: What are the reciprocal functions and cofunction? Do Now: In AB = 17 and BC = 15. 1) Find a) AC b) c) d) 2) Find the reciprocal of a)b) c) A B C.
4.3 Right Triangle Trigonometry Pg. 484 # 6-16 (even), (even), (even) –Use right triangles to evaluate trigonometric functions –Find function.
12-2 Trigonometric Functions of Acute Angles
Quadrant 4 Name that Quadrant…
Bell Work Find all coterminal angles with 125° Find a positive and a negative coterminal angle with 315°. Give the reference angle for 212°.
Lesson 4.2. A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be (1,0) (0,1) (0,-1) (-1,0)
TOP 10 Missed Mid-Unit Quiz Questions. Use the given function values and trigonometric identities to find the indicated trig functions. Cot and Cos 1.Csc.
Section 4.2 Trigonometric Functions: The Unit Circle
13.7 (part 2) answers 34) y = cos (x – 1.5) 35) y = cos (x + 3/(2π)) 36) y = sin x –3π 37) 38) y = sin (x – 2) –4 39) y = cos (x +3) + π 40) y = sin (x.
Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?
4.2 Trigonometric Functions (part 2) III. Trigonometric Functions. A) Basic trig functions: sine, cosine, tangent. B) Trig functions on the unit circle:
Graphs of Other Trigonometric Functions
Graphs of the Trig Functions Objective To use the graphs of the trigonometric functions.
GRAPHS of Trig. Functions. We will primarily use the sin, cos, and tan function when graphing. However, the graphs of the other functions sec, csc, and.
1 What you will learn  How to find the value of trigonometric ratios for acute angles of right triangles  More vocabulary than you can possibly stand!
Section 5.3 Evaluating Trigonometric Functions
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.
Reciprocal functions secant, cosecant, cotangent Secant is the reciprocal of cosine. Reciprocal means to flip the ratio. Cosecant is the reciprocal of.
EXAMPLE 1 Evaluate trigonometric functions given a point Let (–4, 3) be a point on the terminal side of an angle θ in standard position. Evaluate the six.
Warm up Solve for the missing side length. Essential Question: How to right triangles relate to the unit circle? How can I use special triangles to find.
Radian Measure One radian is the measure of a central angle of a circle that intercepts an arc whose length equals a radius of the circle. What does that.
Graphs of other trigonometric functions Section 4.6.
More Trigonometric Graphs
Aims: To know the relationship between the graphs and notation of cosine, sine and tan, with secant, cosecant and cotangent. To be able to state the domain.
Objectives : 1. To use identities to solve trigonometric equations Vocabulary : sine, cosine, tangent, cosecant, secant, cotangent, cofunction, trig identities.
Section 3 – Circular Functions Objective To find the values of the six trigonometric functions of an angle in standard position given a point on the terminal.
Lesson 46 Finding trigonometric functions and their reciprocals.
Warm up. Right Triangle Trigonometry Objective To learn the trigonometric functions and how they apply to a right triangle.
BRITTANY GOODE COURTNEY LEWIS MELVIN GILMORE JR. JESSICA TATUM Chapter 5 Lesson 2.
SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 4.6 Graphs of other Trigonometric Functions.
Bellringer 3-28 What is the area of a circular sector with radius = 9 cm and a central angle of θ = 45°?
Section 4.2 The Unit Circle. Has a radius of 1 Center at the origin Defined by the equations: a) b)
6.7 Graphing Other Trigonometric Functions Objective: Graph tangent, cotangent, secant, and cosecant functions. Write equations of trigonometric functions.
(0, 1 ) (1,0)  (r,0) (0,r) Circle of radius r. (0,1) (1,0)  (r,0) (0,r) (cos ,sin  ) 1.
1. Find the derivatives of the functions sin x, cos x, tan x, sec x, cot x and cosec x. 2. Find the derivatives of the functions sin u, cos u, tan u,
4.4 Day 1 Trigonometric Functions of Any Angle –Use the definitions of trigonometric functions of any angle –Use the signs of the trigonometric functions.
13.1 Right Triangle Trigonometry. Definition  A right triangle with acute angle θ, has three sides referenced by angle θ. These sides are opposite θ,
Right Triangle Trigonometry
Lesson Objective: Evaluate trig functions.
The Other Trigonometric Functions
Introduction to the Six Trigonometric Functions & the Unit Circle
Trigonometric Functions: The Unit Circle Section 4.2
The Unit Circle Today we will learn the Unit Circle and how to remember it.
Pre-Calc: 4.2: Trig functions: The unit circle
2. The Unit circle.
Warm-Up: Give the exact values of the following
Graphing Tangent and the Reciprocal Functions
The Inverse Trigonometric Functions (Continued)
Math /4.4 – Graphs of the Secant, Cosecant, Tangent, and Cotangent Functions.
Trigonometric Functions: The Unit Circle 4.2
9.5: Graphing Other Trigonometric Functions
Academy Algebra II THE UNIT CIRCLE.
Presentation transcript:

Trigonometric functions The relationship between trigonometric functions and a unit circle A.V.Ali

Take a circle with a radius equal to 1 unit Mark a point, A, away from the circle Now draw two tangents from A to the circle A 1

Tangents to the circle Radius of the circle A secant line (the line of a chord through a circle)

sin, cos and tan function

 Radius = 1 1 a b 

  c 1

 cos  sin  tan  Summary

sec, cosec and cot function

 Radius = 1  1  d e

  1 f

 sec  cosec  cot  Summary