Question

All Trigonometric formulae. ​

Answer 1

Answer:

trigonometric formulas

$\sin( \theta) = \frac{opp}{hyp}$

$\cos( \theta) = \frac{adj}{hyp}$

$\tan( \theta) = \frac{opp}{adj}$

$\csc( \theta) = \frac{hyp}{opp}$

$\sec( \theta) = \frac{hyp}{adj}$

$\cot( \theta) = \frac{adj}{opp}$

next,

trigonometric identities

${ \sin( \theta) }^{2} + { \cos( \theta) }^{2} = 1$

${ \sec( \theta) }^{2} - { \tan( \theta) }^{2} = 1$

${ \csc( \theta) }^{2} - { \cot( \theta) }^{2} = 1$

from the first identity

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

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

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

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

from the second identity

${ \sec( \theta) }^{2} = 1 + { \tan( \theta) }^{2}$

$\sec( \theta) = \sqrt{1 + { \tan( \theta) }^{2} }$

${ \tan( \theta) }^{2} = { \sec( \theta) }^{2} - 1$

$\tan( \theta ) = \sqrt{ { \sec( \theta) }^{2} - 1 }$

from the third identity

${ \csc( \theta) }^{2} = 1 + { \cot( \theta) }^{2}$

$\csc( \theta) = \sqrt{ { \sec( \theta) }^{2} - 1 }$

${ \cot( \theta) }^{2} = { \csc( \theta) }^{2} - 1$

$\cot( \theta) = \sqrt{ { \csc( \theta) }^{2} - 1 }$

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Answer 2

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