31Jan

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

sisca05st Mathematics 1 23

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

Posted by sisca05st | Posted at Jan 31, 2020 | Categories: Mathematics

Answers

katiebabyyy
katiebabyyy

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

Jan 31, 2020 21:37

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