A line makes angles α, β, with the coordinate axes. What is sin^2α + sin^2β + sin^2 ?

Three-Dimensional Geometry · Question 12 of 120

Question 12

MediumOriginal question

A line makes angles $\alpha$ , $\beta$ , $\gamma$ with the coordinate axes. What is $\sin^{2}\alpha + \sin^{2}\beta + \sin^{2}\gamma$ ?

0

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1

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2

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3

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CorrectNot quiteAnswer C

Correct answer: C

$\sin^{2}\theta = 1 - \cos^{2}\theta$ , so the sum is $3 - (\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma)$ .
$3 - 1 = 2$ .

Worth noting

1 is the sum of the squared cosines, not of the squared sines.

Ten questions from Three-Dimensional Geometry, at your own pace.

Ten questions from Three-Dimensional Geometry, at your own pace.