Question

Express all trigonometric ratio in term of sintita

Answer 1

there you go :- 
cos a = square root of (1- square of sin a) 
tan = sin a / cos a = sin a/(square root of (1- square of sin a)) 
cosec a = 1/sin a 
sec a = 1/cos a = 1/(square root of (1- square of sin a)) 
cot a = cos a /sin a = (square root of (1- square of sin a))/sin a

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Answer 2

Here we go........

$\sin( \alpha ) = \frac{1}{ \csc( \alpha ) } \\ \\ \sin( \alpha ) = \sqrt{1 - { \cos( \alpha ) }^{2} } \\ \\ \sin( \alpha ) = \cos( \alpha ) \times \tan( \alpha ) \\ \\ \sin( \alpha ) = \cot( \alpha ) \times \cos( \alpha ) \\ \\ \sin( \alpha ) = \cos(90 - \alpha ) \\ \\ \sin( \alpha ) = \frac{perpendicular}{hypotenuse} \\ \\ hope \: help$