Question

10. If cos θ = -2√5/5 , find tan θ.

Answer 1

Answer:

given,

$\cos( \theta) = \frac{ - 2 \sqrt{5} }{5}$

to find

$\tan( \theta)$

we know that

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

$\tan( \theta) = \sqrt{ \frac{1 - {( - 2 \sqrt{5} )}^{2} }{ {( - 2 \sqrt{5} )}^{2} } } \\ \tan( \theta) = \frac{ \sqrt{1 - 20} }{ \sqrt{ {( - 2 \sqrt{5} ) }^{2} } } \\ \tan( \theta) = \frac{ \sqrt{19}i }{ - 2 \sqrt{5} }$

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