How do you evaluate sec(150)?

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How do you evaluate sec(150)?

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Answer 1 · 2018-03-20T14:19:20

$sec 150 = \frac{1}{cos 150} = \frac{1}{cos (180 - 30)} = - \frac{1}{cos 30} = - \frac{1}{\frac{1}{2}} = - 2$ $sec150=1/cos150=1/(cos(180-30))=-1/cos30=-1/(1/2)=-2$

Explanation:

The only difficulty would be in $cos (180 - 30) = - cos 30$ $cos(180-30)=-cos30$ . This is easy to see if we remember the formula $cos (180 - 30) = cos 180 cos 30 + s e n 180 s e n 30 = - 1 \cdot \frac{1}{2} + 0 \cdot \frac{\sqrt{2}}{2} = - cos 30 = - \frac{1}{2}$ $cos(180-30)=cos180cos30+sen180sen30=-1·1/2+0·sqrt2/2=-cos30=-1/2$

Answer 2 · 2018-03-20T14:19:56

$- \frac{2 \sqrt{3}}{3}$ $-(2sqrt3)/3$

Explanation:

$sec 150 = \frac{1}{cos 150}$ $sec150=1/(cos150)$

now

$cos 150 = - cos (180 - 150)$ $cos150=-cos(180-150)$

$cos 30 = \frac{\sqrt{3}}{2}$ $cos30=sqrt3/2$

$:.sec150=1/(-sqrt(3)/2)$

$=-2/sqrt3=-(2sqrt3)/3$

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How do you evaluate sec(150)?

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