Question

If theta is acute and cos²theta =3/4 then the value of sin theta is

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{sin\:\theta=\frac{1}{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline\bold{Given : }} \\ \tt: \implies {cos}^{2} \theta = \frac{3}{4} \\ \\ \red{\underline\bold{To \: Find: }} \\ \tt: \implies sin \: \theta = ?$

• According to given question :

$\tt \circ \: {sin }^{2} \theta + cos^{2} \theta = 1 \\ \\ \tt : \implies {sin}^{2} \theta = 1 - {cos}^{2} \theta \\ \\ \tt: \implies {sin} \: \theta = \sqrt{1 - {cos}^{2} \theta} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies sin \: \theta = \sqrt{1 - {cos}^{2} \: \theta} \\ \\ \tt: \implies sin \: \theta = \sqrt{1 - \frac{3}{4} } \\ \\ \tt: \implies sin \: \theta = \sqrt{ \frac{4 - 3}{4} } \\ \\ \tt: \implies sin \: \theta = \sqrt{ \frac{1}{4} } \\ \\ \green{\tt: \implies sin \: \theta = \frac{1}{2} } \\ \\ \blue{\bold{Some \: trignometrical \: identity}} \\ \orange{\tt \circ \: {tan}^{2} \theta + 1 = {sec}^{2} \theta} \\ \\ \orange{\tt \circ \: {cot}^{2} \theta + 1 = {cosec}^{2} \theta}$

Answer 2

....

$\tt{\huge{\purple{ .................. }}}$

QUESTION -

If theta is acute and cos²theta =3/4 then the value of sin theta is .......

SOLUTION -

From the above Question, we can derive the following information....

The value of theta is acute.

Cos^ 2 ( theta ) = ( 3 / 4 )

Cos ( theta ) = +- ( √3 / 2 )

Here, theta is acute.

So,

Cos ( theta ) = ( √3 / 2 )

=> Theta = Cos Inverse of ( √3 / 2 ) = 60°

Now we know that :

Sin 60° = { 1 / 2 }

So, the value of theta is 60°.

ANSWER :

Theta = 60°

Sin Theta = { 1 / 2}