Explanation From the given figure, it is observed that A ( cos α , sin α ) and B ( cos β , sin β ) are the two distinct points and c is the distance from A to B . Obtain the value of c 2 by law of cosine. c 2 = 1 2 + 1 2 − 2 ( 1 ) ( 1 ) cos ( α − β ) = 2 ( 1 − cos ( α − β ) ) That is, c 2 = 2 ( 1 − cos ( α − β ) ) ( 1 ) The distance between any two point ( x 1 , x 2 ) and ( y 1 , y 2 ) is ( x 1 − y 1 ) 2 + ( x 2 − y 2 ) 2 . Thus, the distance c from ( cos α , sin α ) to ( cos β , sin β ) is c = ( cos α − cos β ) 2 + ( sin α − sin β ) 2

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Chapter A, Problem 85E

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To prove: The subtraction formula cos(α−β)=cosαcosβ+sinαsinβ.

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Chapter A, Problem 84E

Chapter A, Problem 86E

Chapter A Solutions

ESSENTIAL CALCULUS(LL)-W/ACCESS>CUSTOM<

Ch. A - Prob. 1E Ch. A - Convert from degrees to radians. 300 Ch. A - Convert from degrees to radians. 9 Ch. A - Convert from degrees to radians. 315 Ch. A - Convert from degrees to radians. 900 Ch. A - Convert from degrees to radians. 36 Ch. A - Convert from radians to degrees. 4 Ch. A - Convert from radians to degrees. 72 Ch. A - Convert from radians to degrees. 512 Ch. A - Convert from radians to degrees. 83

Ch. A - Convert from radians to degrees. 38 Ch. A - Convert from radians to degrees. 5 Ch. A - Find the length of a circular arc subtended by an...Ch. A - If a circle has radius 10 cm, find the length of...Ch. A - A circle has radius 1.5 m. What angle is subtended...Ch. A - Find the radius of a circular sector with angle...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Draw, in standard position, the angle whose...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the exact trigonometric ratios for the angle...Ch. A - Find the remaining trigonometric ratios. sin=35,02 Ch. A - Find the remaining trigonometric ratios. tan=2,02 Ch. A - Find the remaining trigonometric ratios. sec=1.5,2 Ch. A - Find the remaining trigonometric ratios....Ch. A - Find the remaining trigonometric ratios. cot=3,2 Ch. A - Find the remaining trigonometric ratios....Ch. A - Find, correct to five decimal places, the length...Ch. A - Find, correct to five decimal places, the length...Ch. A - Find, correct to five decimal places, the length...Ch. A - Find, correct to five decimal places, the length...Ch. A - Prove each equation. (a) Equation 10a (b) Equation...Ch. A - Prove each equation. (a) Equation 14a (b) Equation...Ch. A - Prove each equation. (a) Equation 18a (b) Equation...Ch. A - Prove the identity. cos(2x)=sinx Ch. A - Prove the identity. sin(2+x)=cosx Ch. A - Prove the identity. sin(x)=sinx Ch. A - Prove the identity. sincot=cos Ch. A - Prove the identity. (sinx+cosx)2=1+sin2x Ch. A - Prove the identity. secycosy=tanysiny Ch. A - Prove the identity. tan2sin2=tan2sin2 Ch. A - Prove the identity. cot2+sec2=tan2+csc2 Ch. A - Prove the identity. 2csc2t=sectcsct Ch. A - Prob. 51E Ch. A - Prob. 52E Ch. A - Prob. 53E Ch. A - Prob. 54E Ch. A - Prob. 55E Ch. A - Prob. 56E Ch. A - Prob. 57E Ch. A - Prob. 58E Ch. A - Prob. 59E Ch. A - Prob. 60E Ch. A - Prob. 61E Ch. A - Prob. 62E Ch. A - Prob. 63E Ch. A - Prob. 64E Ch. A - Prob. 65E Ch. A - Prob. 66E Ch. A - Prob. 67E Ch. A - Prob. 68E Ch. A - Prob. 69E Ch. A - Prob. 70E Ch. A - Prob. 71E Ch. A - Prob. 72E Ch. A - Prob. 73E Ch. A - Prob. 74E Ch. A - Prob. 75E Ch. A - Prob. 76E Ch. A - Prob. 77E Ch. A - Prob. 78E Ch. A - Prob. 79E Ch. A - Prob. 80E Ch. A - Prob. 81E Ch. A - Prob. 82E Ch. A - Prob. 83E Ch. A - Prob. 84E Ch. A - Prob. 85E Ch. A - Prob. 86E Ch. A - Prob. 87E Ch. A - Prob. 88E Ch. A - Find the area of triangle ABC, correct to five...

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Sine, Cosine and Tangent graphs explained + how to sketch | Math Hacks; Author: Math Hacks;https://www.youtube.com/watch?v=z9mqGopdUQk;License: Standard YouTube License, CC-BY

To prove: The subtraction formula cos ( α − β ) = cos α cos β + sin α sin β .

Solution Summary: The author explains the subtraction formula mathrmcos(alpha -beta 'right') and the distance c from A to B.

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To prove: The subtraction formula cos(α−β)=cosαcosβ+sinαsinβ.

Want to see the full answer?

Chapter A Solutions