Mathematics
sisca05st
2

Suppose theta= 11pi/12. How do you use the sum identity to find the exact value of sin theta?

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(1) Answers
katiebabyyy

The better way is, first we have to find the equivalent in degrees [latex]2\pi=360\º[/latex] [latex]\frac{11\pi}{12}=345\º[/latex] now we can change this value to [latex]-15\º[/latex] how do we get an angle like this?! [latex]30\º-45\º=-15\º[/latex] then [latex]sin(30\º-45\º)=sin(30\º)*cos(45\º)-sin(45\º)*cos(30\º)[/latex] [latex]\begin{Bmatrix}sin(30\º)&=&\frac{1}{2}\\\\sin(45\º)&=&cos(45\º)&=&\frac{\sqrt{2}}{2}}\end{matrix}\\\\cos(30\º)&=&\frac{\sqrt{3}}{2}\end{matrix}[/latex] now we replace this values [latex]sin(-15\º)=\frac{1}{2}*\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2}[/latex] [latex]sin(-15\º)=\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4}[/latex] [latex]\boxed{\boxed{sin(-15\º)=sin(345\º)=\frac{\sqrt{2}-\sqrt{6}}{4}}}[/latex]

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