Question

Q. If sin θ =6/7 and Theta θ is an acute angle. Find the other five trigonometric function value for (θ ).

Answer 1

Step-by-step explanation:

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Answer 2

$Given \: sin \:\theta = \frac{6}{7} \: --(1)$

$i) cos \theta = \sqrt{ 1 - sin^{2} \theta }$

$= \sqrt{ 1 - \Big( \frac{6}{7}\Big)^{2}}$

$= \sqrt{ 1 - \frac{36}{49} }$

$= \sqrt{ \frac{49-36}{49} }$

$= \frac{\sqrt{13}}{7} \: --(2)$

$ii) tan \theta = \frac{sin \theta }{cos \theta}$

$= \frac{ \frac{6}{7}}{\frac{\sqrt{13}}{7}}$

$= \frac{6}{\sqrt{13}} \: --(3)$

$iii) cot \theta = \frac{1}{tan \theta}$

$= \frac{\sqrt{13}}{6}$

$iv ) Cosec \theta = \frac{1}{sin \theta }$

$= \frac{7}{6} \: --(4)$

$v ) Sec \theta = \frac{1}{cos \theta }$

$= \frac{7}{ \sqrt{13}}\: --(5)$

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