Question

sin(π/6+theta)=0.51 find theta ​

Answer 1

Given,

$\[\sin \left( {\frac{\pi }{6} + \theta } \right) = 0.51\]$

Solution,

Calculate the value of $\[\theta \]$

$\[\sin \left( {\frac{\pi }{6} + \theta } \right) = 0.51\]$

$\[ \Rightarrow \left( {\frac{\pi }{6} + \theta } \right) = {\sin ^{ - 1}}0.51\]$

$\[ \Rightarrow \theta = {\sin ^{ - 1}}0.51 - \frac{\pi }{6}\]$

Hence the value of $\[\theta \]$ is $\[{\sin ^{ - 1}}\left( {0.51} \right) - \frac{\pi }{6}\]$

Answer 2

Given: $\[\sin \left( {\frac{\pi }{6} + \theta } \right) = 0.51\]$.

To find: the value of $\theta$.

Solution:

Simplify the given equation.

$\[\sin \left( {\frac{\pi }{6} + \theta } \right) = 0.51\]$

Multiply by $\[{\sin ^{ - 1}}\]$on both sides.

$\[ \Rightarrow {\sin ^{ - 1}}\sin \left( {\frac{\pi }{6} + \theta } \right) = {\sin ^{ - 1}}0.51\]$

$\[\left[ {{{\sin }^{ - 1}}\sin \theta = \theta } \right]\]$

$\[ \Rightarrow \left( {\frac{\pi }{6} + \theta } \right) = {\sin ^{ - 1}}0.51\]$

$\[ \Rightarrow \theta = {\sin ^{ - 1}}0.51 - \frac{\pi }{6}\]$

Hence, the value of $\theta$ is $\[{\sin ^{ - 1}}0.51 - \frac{\pi }{6}\]$.