Question

if theta equals to 30 degree find sin 15 degree

Answer 1

by formula,solving we get answer +- root over 2-√3/4
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Answer 2

Answer:

Here we will find the value of $sin 15\textdegree$ with the help of given theta value $30\textdegree$

Final Answer: $sin15\textdegree=\frac{\sqrt{3}-1 }{2\sqrt{2} }$ or $0.2588$

Step-by-step explanation:

From the given question, $\theta = 30\textdegree$. $sin 15\textdegree=?$

                   $sin 15\textdegree= sin(45\textdegree-30\textdegree)$

Using trigonometric formula, $sin(A-B)=sin AcosB-cosAsinB$

Here $A=45\textdegree$ and $B=30\textdegree$

                    $sin(45\textdegree-30\textdegree)=sin45\textdegree cos30\textdegree-cos45\textdegree sin30\textdegree$

From the trigonometric table,

$sin 45\textdegree=\frac{1}{\sqrt{2} }$, $sin 30\textdegree=\frac{1 }{2}$, $cos45\textdegree=\frac{1}{\sqrt{2} }$ $cos 30\textdegree = \frac{\sqrt{3} }{2}$. Apply this value in the above equation.

                          $sin 15\textdegree=\frac{1}{\sqrt{2} } *\frac{\sqrt{3} }{2}- \frac{1}{\sqrt{2} }*\frac{1}{2}$                  

                                     $=\frac{\sqrt{3} }{2\sqrt{2}}- \frac{1}{2\sqrt{2} }$

Denominator is same. So that it can be written as,

                         $sin15\textdegree=\frac{\sqrt{3}-1 }{2\sqrt{2} }$

The value of $\sqrt{3}=1.732$ and $\sqrt{2}=1.414$. So that above equation is,

                         $sin15\textdegree=\frac{1.732-1 }{2*1.414 }$

                                     $=\frac{0.732}{2.828}$

                          $sin15\textdegree=0.2588$