Is it impossible to compute \frac{11\sin(52)}{\sin(116)} = ? without knowing

Lizeth Jackson

Lizeth Jackson

Answered question

2022-01-28

Is it impossible to compute 11sin(52)sin(116)=? without knowing the exact value of sin52  and  sin116

Answer & Explanation

Brenton Pennington

Brenton Pennington

Beginner2022-01-29Added 15 answers

Assuming you are using degrees, we have sin(116)=sin(90+26)=cos(26) Then
11sin(52)sin(116)=112sin(26)cos(26)cos(26)=22sin(26)
which is simpler but not a decimal answer. After this, you can use a Taylor series centered at sin(30) to get an approximate answer.
Jacob Trujillo

Jacob Trujillo

Beginner2022-01-30Added 13 answers

Note that
sin(90+x)=cosxsin(116)=cos(26)
11sin(52)cos(26)
And recall
sin2x=2sinxcosx
which yields
22sin(26)cos(26)cos(26)=22sin{(26)}
You could estimate using the expansion for sinx perhaps, which doesn’t seem too practical here.
sinx=xx33!+x55!x77!+
Using x=13π90 (in radians) and evaluating the first two or three terms, you can get a decent approximation and multiply the value by 22.

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