Question

(1),find the degree measure corresponding to 11/14(use π = 22/7). (2),if cosX= -1/2, X lies in the third Quadrant ,Find sinX and Tan X.​

Answer 1

Answer:

${1}^{c} = \frac{180°}{\pi}$

${ \frac{11}{14} }^{c} = ( \frac{11}{14} \times \frac{180}{\pi} )° \\ = \frac{11}{14} \times \frac{180}{ \frac{22}{7} } \\ = \frac{11 \times 180 \times 7}{14 \times 22} \\ = 45°$

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$\cos(x) = - \frac{1}{2} \: \\ \sin(x) = \sqrt{1 -cos²(x) } \\ = \sqrt{1 - {( \frac{ - 1}{2} ) }^{2} } \\ = \sqrt{1 - \frac{1}{4} } \\ = \sqrt{ \frac{3}{4} } \\ since, \: x \: lies \: in \: third \: quadrant \: where \: \sin(x )\: is \: negative \: and \tan(x) \: is \: positive\: \ \: so, \\ \sin(x) = - \frac{ \sqrt{3} }{2} \\ \tan(x) = \frac{ \sin(x) }{ \cos(x) } = \frac{ - \frac{ \sqrt{3} }{2} }{ \frac{ - 1}{2} } = \sqrt{3}$