Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the...

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Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π, Phase shift 2π units left, Vertical shift up 2 units and a reflection over the x axis.

Transcript of Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the...

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

Warm Up

1) Are the following functions periodic?

2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π, Phase shift 2π units left, Vertical shift up 2 units and a reflection over the x axis.

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

Reminder!!

Tomorrow go to room 1608 for 2nd period!

Page 3: Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

HW Check

Page 4: 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

AREA OF A SECTOR

Page 5: 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

An arc of a circle is a portion of the circumference formed by a central angle.

It’s the length of the pie crust!

θ

Page 6: 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

The arc length s of a circle radius r, subtended by a central angle of θ radians, is given by:

s = rθ The angle must ALWAYS BE IN

RADIANS. Sometimes it will be given in

degrees to trick you. Convert it to radians!

Page 7: Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian.

Example 1: Arc Length

“Subtended?” That just means

“formed by.”

Page 8: Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Area of a Sector

A sector of a circle is a portion of the circle formed by a central angle.

It’s the area of a slice of pie!

θ

Page 9: Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Area of a Sector

The area of a sector A of a circle radius r, subtended by a central angle of θ radians, is given by:

A = ½r2θAgain, the angle must

ALWAYS BE IN RADIANS. Sometimes

it will be given in degrees to trick you. Convert it to radians!

Page 10: Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Find the area of the sector of a circle of radius 5 feet subtended by an angle of 60°. Round the answer to two decimal places.

Example 2: Area of a Sector

“Subtended?” That just means

“formed by.”

Page 11: Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Put it all together!Arc Length Area of a Sectors = rθ A = ½r2θLength of pie crust Area of a slice

Page 12: Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Unit 4 Review Sheet


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Untitled-2 []”π” ”π— ß“π ≥– √√¡ “√ “√»÷ …“¢—Èπæ Èπ∞“π¡’Àπâ“∑’Ë √—∫º ‘¥ Õ∫„π “√‡∑’¬∫«ÿ

AUDIO COMPRESSION USING MODIFIED DISCRETE COSINE · PDF fileAUDIO COMPRESSION USING MODIFIED DISCRETE COSINE TRANSFORM: ... entitled Audio Compression Using Modified Discrete Cosine

AUDIO COMPRESSION USING MODIFIED DISCRETE COSINE · PDF fileAUDIO COMPRESSION USING MODIFIED DISCRETE COSINE TRANSFORM: ... entitled Audio Compression Using Modified Discrete Cosine

Dynamic nonlinear elasticity in geomaterials€¦ · DYNAMIC NONLINEAR ELASTICITY IN GEOMATERIALS 3 x σ = 0 σ = 1-π-π π π x σ = _ σ = 4-π-π π π 2 π x σ >> 1-π π Amplitude

Dynamic nonlinear elasticity in geomaterials€¦ · DYNAMIC NONLINEAR ELASTICITY IN GEOMATERIALS 3 x σ = 0 σ = 1-π-π π π x σ = _ σ = 4-π-π π π 2 π x σ >> 1-π π Amplitude

XIV International Conference on Hadron Spectroscopy · 10608.1 ± 1.7 10653.3 ± 1.5 10888.4 ± 3.0 15.5 ± 2.4 14.0 ± 2.8 30.7+8.0 −7.7 Υ(nS)π+π− Υ(nS)π+π− n =1, 2,

XIV International Conference on Hadron Spectroscopy · 10608.1 ± 1.7 10653.3 ± 1.5 10888.4 ± 3.0 15.5 ± 2.4 14.0 ± 2.8 30.7+8.0 −7.7 Υ(nS)π+π− Υ(nS)π+π− n =1, 2,

Calculus flash cards - California State University, Fresnozimmer.csufresno.edu/~lburger/Calculus flash cards.pdfcos 2 π 1 tan θ (in terms of sine and/or cosine) sin cos θ θ cot

Calculus flash cards - California State University, Fresnozimmer.csufresno.edu/~lburger/Calculus flash cards.pdfcos 2 π 1 tan θ (in terms of sine and/or cosine) sin cos θ θ cot

trigonometry - iiw.kuleuven.be · 5.2 The cosine rules ... Beside sine and cosine other trigonometric numbers are defined as follows : ... 2.5.2 Proof the following identity

trigonometry - iiw.kuleuven.be · 5.2 The cosine rules ... Beside sine and cosine other trigonometric numbers are defined as follows : ... 2.5.2 Proof the following identity

ƒπ•∏ ∫∞π ∫π¡∏™∏ ™∆∞ ∞™¶√¡¢À§∞users.sch.gr/mchatzinik/biologiaAgymnasiou/Biblia/math... · 2011. 7. 11. · 102 µπ√§√°π∞ ∞’ °Àª¡∞™π√À

ƒπ•∏ ∫∞π ∫π¡∏™∏ ™∆∞ ∞™¶√¡¢À§∞users.sch.gr/mchatzinik/biologiaAgymnasiou/Biblia/math... · 2011. 7. 11. · 102 µπ√§√°π∞ ∞’ °Àª¡∞™π√À

cover-2 · 2012-10-26 · ’ˇ° ‘¥®“°ª√ ‘μ 294 ‡¢â“„®« à“∑ —Èß 2 ‡™ ÈÕπ ’ȇª ìπ§π≈–™π ‘¥° —π ®π ...

cover-2 · 2012-10-26 · ’ˇ° ‘¥®“°ª√ ‘μ 294 ‡¢â“„®« à“∑ —Èß 2 ‡™ ÈÕπ ’ȇª ìπ§π≈–™π ‘¥° —π ®π ...

π - Indico - CERN

π - Indico - CERN

Unit 5 – CHAPTER 4: Graphing · 1 -1 2 π − Trigonometry B: Unit 5: Chapter 4 – Graphing Trig E quations Date: Notes – Day 3: Sine & Cosine Graph Horizontal (Phas e) Shifts

Unit 5 – CHAPTER 4: Graphing · 1 -1 2 π − Trigonometry B: Unit 5: Chapter 4 – Graphing Trig E quations Date: Notes – Day 3: Sine & Cosine Graph Horizontal (Phas e) Shifts

TheContragredient - Department of Mathematics - Homejda/preprints/contragredient.pdf · 2012-12-14 · Conjecture 1.2 If Π is an L-packet, then so is Π∗ = {π∗ |π∈ Π}. The

TheContragredient - Department of Mathematics - Homejda/preprints/contragredient.pdf · 2012-12-14 · Conjecture 1.2 If Π is an L-packet, then so is Π∗ = {π∗ |π∈ Π}. The

Calculus flash cards - Weeblypatemath.weebly.com/uploads/5/2/5/8/52589185/calculus_flash_cards.pdfcos 2 π 1 tan θ (in terms of sine and/or cosine) sin cos θ θ cot θ (in terms

Calculus flash cards - Weeblypatemath.weebly.com/uploads/5/2/5/8/52589185/calculus_flash_cards.pdfcos 2 π 1 tan θ (in terms of sine and/or cosine) sin cos θ θ cot θ (in terms

Microfibers Synthesized by Wet-Spinning of Chitin ... · beginning of the range used for the calculation of the average cosine ‹cos2φ›. S was calculated at φ 0 of 0, π/2, π

Microfibers Synthesized by Wet-Spinning of Chitin ... · beginning of the range used for the calculation of the average cosine ‹cos2φ›. S was calculated at φ 0 of 0, π/2, π

GAME-1* · 6 The Hunger Games §”π” ‡¥Á°Àπÿà¡ “«‡¢â“ Ÿà π“¡·¢àߢ—π ‡æ ËÕÀ“º Ÿâ™π–--§π ÿ¥∑⓬´÷Ë߬ πÀ¬—¥

GAME-1* · 6 The Hunger Games §”π” ‡¥Á°Àπÿà¡ “«‡¢â“ Ÿà π“¡·¢àߢ—π ‡æ ËÕÀ“º Ÿâ™π–--§π ÿ¥∑⓬´÷Ë߬ πÀ¬—¥

Dalitz analysis of the decay * B + →π + π - π +

Dalitz analysis of the decay * B + →π + π - π +

Opinion Analyzer Internet Review Opinion Mining and Data … · all the review and calculated by cosine similarity. Cosine similarity can be resulted as following when we have ‘n’

Opinion Analyzer Internet Review Opinion Mining and Data … · all the review and calculated by cosine similarity. Cosine similarity can be resulted as following when we have ‘n’

Π Π - w5. · PDF fileΠ Π Π Π 7kt5 501 7kt5 502 7kt5 504 7kt5 602 7kt5 604

Π Π - w5. · PDF fileΠ Π Π Π 7kt5 501 7kt5 502 7kt5 504 7kt5 602 7kt5 604

Use Cosine

Use Cosine

000 Cover€¦ · §”π”¢Õߧ—¡¿’√å [5] ‡À¡ Õπ™â“ßµ“∫Õ¥‡∑’ˬ«‰ª„πªÉ“©–π—Èπé «‘π“ π‘√ÿµ⁄µ‘꓇≥π

000 Cover€¦ · §”π”¢Õߧ—¡¿’√å [5] ‡À¡ Õπ™â“ßµ“∫Õ¥‡∑’ˬ«‰ª„πªÉ“©–π—Èπé «‘π“ π‘√ÿµ⁄µ‘꓇≥π

Introducing Bayesian Argumentation Networks...Bayesian Argumentation Networks thentheprobabilityofe canbecalculatedas π(X) ·π(Y) ·(1 −π(A)) ·π(U) ·(1 −π(W))3 The version

Introducing Bayesian Argumentation Networks...Bayesian Argumentation Networks thentheprobabilityofe canbecalculatedas π(X) ·π(Y) ·(1 −π(A)) ·π(U) ·(1 −π(W))3 The version