Question

Please help!!

The Pythagorean Identity states that:
(sin x)2 + (cos x)2 = 1
Given cos 0 = 9/10, find sin 0.
sin 0 = [ ? ] / [ ? ]
Simplify the fraction

Answer 1

`sin \theta = \frac{\sqrt {19}}{10}`

Explanation:

`( \sin \theta) ^(2) + ( \cos \theta) ^(2) = 1 \\ \\ \therefore \:( \sin \theta) ^(2) + { \bigg( \frac{{9} }{10} \bigg)}^(2)= 1 \\ \\( \sin \theta) ^(2) + (81)/(100)= 1 \\ \\ ( \sin \theta) ^(2) = 1 - (81)/(100) \\ \\ ( \sin \theta) ^(2) = (100 - 81)/(100) \\ \\ ( \sin \theta) ^(2) = (19)/(100) \\ \\ \sin \theta = \sqrt{(19)/(100) } \\ \\ \sin \theta = \frac{\sqrt {19}}{10}`