Question

If cos O = 0.6 find the value of 5 sin thita - 3 tan thita​

Answer 1

Note: Just for comfort yout theta = my alpha.

We have,

$\cos( \alpha ) = 0.6$


Using,
${ \sin}^{2} + { \cos}^{2} \alpha = 1$

We have,

${ \sin }^{2} \alpha + 0.36 = 1 \\ \\ { \sin }^{2} \alpha = 0.64 \\ \sin( \alpha ) = 0.8$


using these,
$5 \sin( \alpha ) - 3 \tan( \alpha ) \\ \\ = 5 \sin( \alpha ) - (3 ) \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ \\ = 5(0.8) - (3 )\frac{0.8}{0.6} \\ \\ = 4.0 - 0.4 \\ \\ = 3.6$


Therefore, 3.6 is your answer.