Question

if 2 cos theta equal to root 3 then find all trigonometric ratios of angle theta ​

Answer 1

Question:

If 2 cosθ = √3, then find all trigonometric ratios of angle θ.

Given:

• 2 cosθ = √3

To find:

• All trigonometric ratios of angle θ.

Solution:

$2cos \: θ = \sqrt{3} \\ cos \:θ = \frac{ \sqrt{3} }{2}$

By the Pythagoras theorem,

$x = \sqrt{ {2}^{2} - \sqrt{ {3}^{2} } } \\ \\ = \sqrt{4 - 3} \\ \\ = \sqrt{1} \\ \\</u></strong><strong><u>=</u></strong><strong><u> 1$

Therefore,

$\sinθ = \frac{1}{2} \\ \\ \cosθ = \frac{ \sqrt{3} }{2} \\ \\ \tanθ = \frac{1}{ \sqrt{3} } \\ \\ \cosecθ = 2 \\ \\ \secθ \: = \frac{2}{ \sqrt{3} } \\ \\ \cotθ = \sqrt{3}$

Hope it helps ya!!

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