Question

if Cos A = 1/2 , A lies In Q4, Find all other T-functions

Answer 1

Question:-

If

$\cos \: A = \frac{1}{2}$

A lies in Q 4 ,find all other trigonometric functions

Solution:-

Given,

$\cos \: </strong><strong>A</strong><strong> = \frac{1}{2}$

We know that,

$(hypotenuse)^{2} = {(side)}^{2} + {(side)}^{2}$

${(side)} = \sqrt{( {hypotenuse)}^{2} - {(side)}^{2} }$

$side = \sqrt{ {2}^{2} - {1}^{2} }$

$side = \sqrt{3}$

In Q4 only cosine and secant are positive

So,

$\sin \: A = - \frac{ \sqrt{3} }{2}$

$\tan \: A = - \frac{ \sqrt{3} }{1} = - \sqrt{3}$

$\cot \: A = - \frac{1}{ \sqrt{3} }$

$\sec \: A = \frac{2}{1} = 2$

$\csc \: A = - \frac{2}{ \sqrt{3} }$