Solve sec x = 1.788, 0°<x<720° ?

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Solve sec x = 1.788, 0°<x<720° ?

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Answer 1 · 2018-05-21T23:54:39

$60^{\circ}, 300^{\circ}; 420^{\circ}; 660^{\circ}$ $60^@, 300^@; 420^@; 660^@$

Explanation:

sec x = 1.788
$cos x = \frac{1}{sec x} = \frac{1}{1.788} = 0.559$ $cos x = 1/(sec x) = 1/1.788 = 0.559$ .
Calculator and unit circle give 2 solutions for x -->
$x = \pm 60^{\circ} + k 360^{\circ}$ $x = +- 60^@ + k360^@$
Note: $x = - 60^{\circ}$ $x = - 60^@$ is co-terminal to $x = 300^{\circ}$ $x = 300^@$
Answers for (0, 720):
$x = 60^{\circ}, x = 300^{\circ}; x = 420^{\circ}; x = 660^{\circ}$ $x = 60^@, x = 300^@; x = 420^@; x = 660^@$

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Solve sec x = 1.788, 0°<x<720° ?

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