BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter C, Problem 41E
To determine

To prove: The Law of Cosines.

Expert Solution

Explanation of Solution

From the given figure, it is observed that x=bcosθandy=bsinθ.

The distance between any two point (x1,x2)and(y1,y2) is (x1y1)2+(x2y2)2.

Thus, the distance c from (x,y)to(a,0) is c=(xa)2+(y0)2.

Further simplified as,

c2=(xa)2+(y0)2=(bcosθa)2+(bsinθ0)2=b2cos2θ+a22abcosθ+b2sin2θ=a2+b2(cos2θ+sin2θ)2abcosθ=a2+b22abcosθ

That is, c2=a2+b22abcosθ.

Hence the proof.

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