'Cos 3' presentation slideshows

OUTLINE ___________________________________________________________ ? INTRODUCTION

Effects of atmospheric turbulence on azimuths and grazing angles estimation at the long distances from explosions Sergey Kulichkov Igor Chunchuzov Gregory Bush Vladimir Asming Elena Kremenetskaya Anatoly Barishnokov Yurii Vinogradov Supported by RFBR, project No. 08-05-00445. OUTLINE

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B ? D ( * ) K GLW, ADS

B ? D ( * ) K GLW, ADS. Y. Horii (Nagoya) and K. Trabelsi (KEK). Referees: Z. Dolezal, N. Muramatsu, K. Sakai. Thanks to very active refereeing!. ? 3 from B ? D (*) K decays. _. Tree-level ? 3 determination from interference of B ? DK and B ? DK amplitudes.

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Visualizing High-Order Surface Geometry

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Double-Angle, Half-Angle, and Product-Sum Formulas

Double-Angle, Half-Angle, and Product-Sum Formulas. The identities we consider in this section are consequences of the addition formulas. The Double-Angle Formulas allow us to find the values of the trigonometric functions at 2 x from their values at x .

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1.5 Using the Definitions of the Trigonometric Functions

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Spherical and cylindrical coordinates

Math 200 Week 8 - Friday. Spherical and cylindrical coordinates. Math 200. Be able to convert between the three different coordinate systems in 3-Space: rectangular, cylindrical, spherical Develop a sense of which surfaces are best represented by which coordinate systems. Goals.

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Barnett/Ziegler/Byleen Precalculus: A Graphing Approach

Barnett/Ziegler/Byleen Precalculus: A Graphing Approach. Chapter Seven Additional Topics in Trigonometry. Law of Sines. The law of sines is used to solve triangles, given: 1. Two angles and any side (ASA or AAS), or 2. Two sides and an angle opposite one of them (SSA). sin. sin. sin. ?.

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8.2

8.2. SINUSOIDAL FUNCTIONS AND THEIR GRAPHS. Amplitude and Midline. The functions y = A sin t + k and y = A cos t + k have amplitude | A | and the midline is the horizontal line y = k. Amplitude and Midline. Example 1

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Repeats every 360 o

Y = Sin q. Repeats every 360 o. 2 solutions every 360 o. Y = Cos q. Repeats every 360 o. 2 solutions every 360 o. Y = Tan q. Repeats every 180 o. 1 solution every 180 o. All. Sin. Tan. Cos. Y = Sin 3 q. There are 6 solutions except for when sin 3 q = 1 or -1. Cos 3 q = 0.5602.

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Differentiation in Polar Coordinates

Differentiation in Polar Coordinates. Lesson 10.7. Review. Relationship of polar and rectangular systems x = r cos ? y = r sin ? Given r = f( ? ), simple to find dr/d ? However, we seek dy/dx. Finding dy/dx. We know r = f( ? ) and y = r sin ? and x = r cos ? Then And.

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Clicker Question 1

Clicker Question 1. What is ? x sin(3 x ) d x ? A. (1/3)cos(3 x ) + C B. (-1/3) x cos(3 x ) + (1/9)sin(3 x ) + C C. - x cos(3 x ) + sin(3 x ) + C D. -3 x cos(3 x ) + 9sin(3 x ) + C E. (1/3) x cos(3 x ) - (1/9)sin(3 x ) + C. Clicker Question 2. What is ?

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( cos ? + i sin?) 3 = ( cos ? + i sin?) ( cos ? + i sin?) ( cos ? + i sin?)

To Prove: Cos 3 ? =c os 3 ? - 3 sin 2 ? cos ? and Sin3 ? = sin ? - 4 sin 3 ?. Proof:. ( cos ? + i sin?) 3 = ( cos ? + i sin?) ( cos ? + i sin?) ( cos ? + i sin?). = ( cos 2 ? + i sin? cos ? + i sin ? cos ? + i 2 sin 2 ?)( cos ? + i sin?).

119 views • 1 slides