Polar Emi, Grace, Susan.

Slides:

Advertisements

Similar presentations

Remember: Derivative=Slope of the Tangent Line.

Advertisements

Parametric Equations t x y

Equations of Tangent Lines

Lengths of Plane Curves

Find the period of the function y = 4 sin x

Chapter 14 Section 14.3 Curves. x y z To get the equation of the line we need to know two things, a direction vector d and a point on the line P. To find.

Polar Graphs and Calculus

3.8 Derivatives of Inverse Trigonometric Functions.

W-up Get out note paper Find 12.3 notes

Equations of Tangent Lines April 21 st & 22nd. Tangents to Curves.

10.3 Polar Coordinates. Converting Polar to Rectangular Use the polar-rectangular conversion formulas to show that the polar graph of r = 4 sin.

Using Polar Coordinates Graphing and converting polar and rectangular coordinates.

10.4A Polar Equations Rectangular: P (x, y) Polar: P (r,  )  r = radius (distance from origin)   = angle (radians)

3.5 Derivatives of Trig Functions. Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine.

10.1 Parametric Equations. In chapter 1, we talked about parametric equations. Parametric equations can be used to describe motion that is not a function.

10.2 – 10.3 Parametric Equations. There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations.

Tangent Lines and Arc Length Parametric Equations

If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

3.9: Derivatives of Exponential and Logarithmic Functions.

Differentiation By: Doug Robeson. What is differentiation for? Finding the slope of a tangent line Finding maximums and minimums Finding the shape of.

10.4 Polar Coordinates Miss Battaglia AP Calculus.

Today in Precalculus Go over homework Notes: Graphs of Polar Equations Homework.

+. + 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.

Conics, Parametric Equations, and Polar Coordinates 10 Copyright © Cengage Learning. All rights reserved.

Copyright © 2005 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 6.3 Lengths of Plane Curves (1 st lecture of week 10/09/07- 15/09/07)

Conics, Parametric Equations, and Polar Coordinates 10 Copyright © Cengage Learning. All rights reserved.

WRITING EQUATIONS IN SLOPE INTERCEPT FORM 4.2. What you need… ■In order to write an equation in slope intercept form you need to know 2 things: ■ y =

The 3 Great Trigonometric Properties. Draw 50 O in Standard Position X Y 50 O y r x P(x,y)

10.6B and 10.7 Calculus of Polar Curves.

How big is my heart??? (Find the area of the enclosed region) WARM UP - Calculator active.

Lesson: ____ Section: 3.7  y is an “explicitly defined” function of x.  y is an “implicit” function of x  “The output is …”

Warm Up. Equations of Tangent Lines September 10 th, 2015.

Clear your desk for the Quiz. Arc Length & Area Arc Length The length of a continuous curve r(θ) on the interval [  ] is equal to.

FRQ Review. Test Review Retakes by Wed FRQs 7(AB) or 10(BC) types 6 questions per year 9 points each Questions 1 and 2 – calculator Questions 3-6 – non.

Tangent Lines and Arc Length Parametric Equations

Ch. 11 – Parametric, Vector, and Polar Functions 11.3 – Polar Functions.

10 Conics, Parametric Equations, and Polar Coordinates

Implicit Differentiation

Implicit Differentiation

MATH 1330 Polar Coordinates.

Implicit Differentiation

Tangent Lines and Arc Length Parametric Equations

Vector-Valued Functions and Motion in Space

Today in Precalculus Go over homework Need a calculator

14.3 Trigonometric Identities

Double Integrals with Polar Coordinates

Sum and Difference Identities

Sum and Difference Identities for the Sin Function

Using Polar Coordinates

Chapter 9 Review.

Differentiation in Polar Coordinates

Graph and Write Equations of Circles

By Kevin Dai, Minho Hyun, David Lu

5.3/5.4 – Sum and Difference Identities

Derivatives of Inverse Trig Functions

START UP DAY 62 Kirby hits a ball when it is 4 ft above the ground with an initial velocity of 120 ft/sec. The ball leaves the bat at a 30° angle with.

Parametric Equations and Calculus

Areas and Arc Lengths in Polar Form

True or False: The exact length of the parametric curve {image} is {image}

10.2 – Calculus with Parametric Curves

The Chain Rule Section 3.6b.

11.1: Length of a Curve.

9.7 Graphs of Polar Equations

Integration Techniques

8.3 Trigonometric Identities (Part 2)

True or False: The exact length of the parametric curve {image} is {image}

Parametric and Vectors

Sherin Stanley, Sophia Versola

Diff-Eqs and Slope Fields

Plane Curves and Parametric Equations

Presentation transcript:

Polar Emi, Grace, Susan

Card 69: Common Polar Graphs/Equations (1/3)

Card 69: Common Polar Graphs/Equations (2/3) n petals if n is odd, 2n petals if n is even

Card 69: Common Polar Graphs/Equations (3/3)

Card 70: Polar Conversion Formulas x2+y2=r2 or r=√(x2+y2) y=rsin𝛳 or sin𝛳=y/r x=rcos𝛳 or cos𝛳=x/r tan𝛳=y/x or 𝛳=tan-1(y/x)

Card 71: Power Reducing Identities

Card 72: Finding Polar Area

Card 73: Arc Length (Polar)

Card 74: Finding dy/dx (Polar) *don’t forget product rule!

Card 75: Tangent Line (Polar) Find the slope at the given 𝜃, using the formula: Find r and r ’ Plug in given 𝜃 into r and r’ Plug values of r and r’ into the slope formula above Solve for slope Plug the slope and point at 𝜃 into the point slope form of a tangent line:

Card 76: Interpreting Motion (Polar) Particle motion in polar is determined by the rate of the r(𝜃) function: If > 0 then the particle is moving away from the origin If < 0 then the particle is moving towards the pole (origin) If = 0 then the particle’s position MAY be at a maximum distance from the pole (origin) **particle’s distance from the origin is not changing** **the curve is moving away from the origin; r is increasing (when asked about r or the curve) **the curve is approaching the origin; r is decreasing

Homework: Polar Packet: MC: #8 FRQ: #10