Question

If sin theta =root 3 by 2. Find all the trigonometric ratios of thetha

Answer 1

SolutioN :

$\tt \dagger \: \: \: \: \: \fbox{Sin \theta = \dfrac{ \sqrt{3} }{2}}$

With know, Sin 60° = √3 / 2.

$\tt : \implies Sin \theta = \dfrac{ \sqrt{3} }{2}$

$\tt : \implies Sin \theta = sin \: 60 \degree$

$\tt : \implies \theta = 60 \degree$

We have,

• P = √3.
• B = ?
• H = 2.

$\rule{100}2$

★ Let's find value of Base ( By Pythagoras theorem )

$\tt : \implies H^2 = P^2 + B^2.$

$\tt : \implies \big(2 \big)^2 = \big( \sqrt{3} \big)^2 + B^2.$

$\tt : \implies 4= 3 + B^2.$

$\tt : \implies B^2 = 1.$

$\tt : \implies B = \sqrt{1}$

$\tt : \implies B = 1.$

★ Let's Find Trigonometry Ratio.

• Sin theta = √3 / 2.
• Cos theta = 1 / 2.
• tan theta = √3.
• Cosec theta = 2 /√3.
• Sec theta = 2.
• Cot theta = 1 / √3.

$\rule{100}2$

VerificatioN :

• The value of theta = 60° ( Find above )

So,

We are notice,

• Sin 60° = √3 / 2.
• Cos 60° = 1 / 2.
• tan 60° = √3.
• Cosec 60° = 2 /√3.
• Sec 60° = 2.
• Cot 60° = 1 / √3.

Hence Verify.