Chapter 10: Q .51. (page 812)

In Exercises 49-51, two direction cosines are given. Use Exercise 48 to find the third direction cosine.
$51. \cos α = \frac{1}{2}, \cos γ = \frac{\sqrt{3}}{4} .$

Short Answer

Expert verified

$the value of the third directicn cosine is \pm \frac{3}{4}$

Step by step solution

Step 1:Given information

$\cos α = \frac{1}{2}, \cos γ = \frac{\sqrt{3}}{4} .$

Step 2:Simplification

$Consider the drection cosines \cos α = \frac{1}{2}, \cos γ = \frac{\sqrt{3}}{4} .$

$The objective is to fnd the third direction cosine using the result Consider the direction cosinas$

$\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 .$

$Also, \cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$

width="234" height="45" role="math">Nos,sincecosα=12,cosγ=34

$Subetituse the values in (1)$

${(\frac{1}{2})}^{2} + \cos^{2} β + {(\frac{\sqrt{3}}{4})}^{2} = 1$

$\frac{1}{4} + \cos^{2} β + \frac{3}{16} = 1$

$\frac{4 + 3}{16} + \cos^{2} β = 1$

$\frac{7}{16} + \cos^{2} β = 1$

$\cos^{2} β = 1 - \frac{7}{16}$

$= \frac{16 - 7}{16}$ $= \pm \frac{9}{16}$

$\cos γ = \pm \sqrt{\frac{9}{16}}$

$= \pm \frac{3}{4}$

$the value of the third directicn cosine is \pm \frac{3}{4}]$

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In Exercises 49-51, two direction cosines are given. Use Exercise 48 to find the third direction cosine.
$51. \cos α = \frac{1}{2}, \cos γ = \frac{\sqrt{3}}{4} .$

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

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In Exercises 49-51, two direction cosines are given. Use Exercise 48 to find the third direction cosine.51.cosα=12,cosγ=34.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Pure Maths

Mechanics Maths

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

In Exercises 49-51, two direction cosines are given. Use Exercise 48 to find the third direction cosine.
$51. \cos α = \frac{1}{2}, \cos γ = \frac{\sqrt{3}}{4} .$