Question

if 3sin²theta=2 ¼, find the value of theta​

Answer 1

Answer:

Answer is theta is 60°.

Step-by-step explanation:

3 sin²theta = 9/4

sin² theta = 9/12

sin theta = root 3/2

theta = 60°

Answer 2

Given

3sin²theta=2¼

To Find

we have to find the value of theta

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Write given value as it is

=>3sin²theta = 2¼

=>3sin²theta= 4×2+1/4

=>3sin²theta=8+1/4

=>3sin²theta=9/4

=>sin²theta=9/4÷3

=>sin²theta=9/12

=>sin²theta=3/4

=>sintheta=√3/4

=>sintheta= √3/2 [√4=2]

We know that sin60°=√3/2

so, sintheta=sin60°

=>theta=60°

Extra information=>

Other trigonometric values

Note: kindly check on web for better presentation

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$