Arc Length Area of a Sector Unit Circle Trig values of unit circle

Slides:

Advertisements

Similar presentations

Accelerated Math 2.  Two minor arcs are congruent if and only if their corresponding chords are congruent.

Advertisements

Circles Review Unit 9.

Trig – Section 2 The Unit Circle

(1,0) (0,1) (-1,0) (0, -1) α (x,y) x y 1 sin(α) = y cos(α) = x (cos(α), sin(α)) (0,0) tan(α) = y/x 2.1 Unit Circle.

Radians In a circle of radius 1 unit, the angle  subtended at the centre of the circle by the arc of length 1 unit is called 1 radian, written as 1 rad.

Finding Exact Values of Trig Ratios. Special Right Triangles

13-3: Radian Measure Radian Measure There are 360º in a circle The circumference of a circle = 2r. So if the radius of a circle were 1, then there a.

Copyright © 2011 Pearson Education, Inc. Radian Measure, Arc Length, and Area Section 1.2 Angles and the Trigonometric Functions.

Radian Measure. Many things can be measured using different units.

Try describing the angle of the shaded areas without using degrees.

Circumference Arc Radius Diameter Chord Tangent Segment Sector

Aim: How do we define radians and develop the formula Do Now: 1. The radius of a circle is 1. Find, in terms of the circumference. 2. What units do we.

Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Arc Length and Sector Area. How do we get the fraction in these formulas? How many degrees are in a circle? Fraction = (central angle/360)

RADIANS Radians, like degrees, are a way of measuring angles.

Trigonometric Functions sine, cosine and tangent.

And because we are dealing with the unit circle here, we can say that for this special case, Remember:

1 8.1 Inverse Trigonometric Functions In this section, we will study the following topics: Definitions of the inverse trig functions Evaluating inverse.

Arc Length Start with the formula for radian measure … … and multiply both sides by r to get … Arc length = radius times angle measure in radians.

Objective: use the Unit Circle instead of a calculator to evaluating trig functions How is the Unit Circle used in place of a calculator?

Warm up. Review for chapter test Chapter 4 Understanding Trigonometric Functions Language Objectives: We will learn more about trigonometric functions.

Review Trig Functions. Vocab 1) The number of radians in one revolution is _______. 2) Sine and cosine are both negative in the ____ quadrant.

Ch. 6: Trig Functions of Angles James Michel Matthis Feischen Boris Krassovski.

Acute Ratios Reference Angles Exact.

Trigonometry Section 4.2 Trigonometric Functions: The Unit Circle.

1° = 60 ′ 1 ′ = 60 ″ Convert 50°6 ′ 21 ″ 50° + 6 × (1/60)° + 21 × (1/60) × (1/60)° = ° Convert to degrees 21° +.256(60 ′ ) 21° ′

Perimeter and Area with Circles. Circumference of a Circle Circumference is the perimeter of the circle Formula: or (for exact answers, leave π in your.

Sections Perimeter and Area with Circles.

MATH 1330 Section 5.1a. Trigonometric Functions of Real Numbers In this section there is nothing new as far as evaluating trigonometric functions. The.

Trigonometry, 1.0: Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.

Chapter 5 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Trigonometric Functions of Real Numbers; Periodic Functions.

More Trig - Radian Measure and Arc Length Warm-up Learning Objective: To convert from degree measure to radian measure and vice versa and to find arc length.

10-7 Area of Circles and Sectors. REVIEW Circumference: The total distance (in length) around a circle. Arc measure: The measure of the central angle.

Arcs, Sectors & Segments

C2 TRIGONOMETRY.

MATH 1330 Section 5.1.

Aim: How do we define radians and develop the formula

The Trigonometric Functions

Notes 6-1: Radian Measure

Chapter 1 Angles and The Trigonometric Functions

Examples Radians & Degrees (part 2)

16. Find the value of x. x○ 170○.

All pupils can use radian measure in a variety of situations

Warm Up Write an equation for a cosine function with the following characteristics. Amplitude: 4 Period:  Phase shift: left 3 Vertical shift: down 4.

Arc length and area of a sector.

Test is next class Test is open note

Trig Functions and Acute Angles

Sine, Cosine and Tangent - Degrees

MATH 1330 Section 5.1a.

Bell Ringer How many degrees is a radian?

Convert the following angle to radians or vice versa.

Trigonometric Functions

47.75⁰ Convert to radians: 230⁰.

Unit 6 Day 2 Circle Relationships.

6.1 Angles and Radian Measure

Chapter 2 Section 1.

Evaluating Inverse Trig Expressions

Lesson The Unit Circle Objectives:

Chapter 2 Section 1.

Trigonometric Functions: Unit Circle Approach

Trigonometry - Intro Ms. Mougharbel.

( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )

Trig Graphs and reciprocal trig functions

Unit 4: Circles and Volume

Essential Questions: Standards:

Academy Algebra II THE UNIT CIRCLE.

What is the radian equivalent?

Presentation transcript:

Arc Length Area of a Sector Unit Circle Trig values of unit circle Module 6.2 Arc Length Area of a Sector Unit Circle Trig values of unit circle

Length of an arc (Degrees) An arc is part of a circle (part of the circumference) c=2𝜋𝑟 Arc length = 𝑥° 360° ∙2𝜋𝑟 Examples:

Length of an arc (Radians) Arc length = 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 2𝜋 ∙2𝜋𝑟 Arc Length =𝑟𝑎𝑑𝑖𝑎𝑛𝑠∙𝑟 Example:

Area of a sector (Degrees) A sector a “slice” of a circle (Part of the area) Area of a circle = 𝜋 𝑟 2 Area of a sector = 𝑥° 360 ∙𝜋 𝑟 2 Example:

Area of a sector (Degrees) Example:

Find the values of each sine and cosine 𝑠𝑖𝑛60° 𝑠𝑖𝑛225° 𝑠𝑖𝑛 𝜋 2 𝑠𝑖𝑛 7𝜋 3 𝑐𝑜𝑠135° 𝑐𝑜𝑠630° 𝑐𝑜𝑠 7𝜋 6 𝑐𝑜𝑠 14𝜋 6

Find the values of each tangent 𝑡𝑎𝑛 315° 𝑡𝑎𝑛 270° 𝑡𝑎𝑛 5𝜋 6 𝑡𝑎𝑛 9𝜋 4