Trigonometric equation using compound angle formula If arcsin(12/13)+arccos(4/5)=arcsin(k) Use the compound angle formula sin(x+y)=sin(x)cos(y)+cos(x)sin(y) to find the exact value of k

Brooke Richard

Brooke Richard

Answered question

2022-11-19

trigonometric equation using compound angle formula
If arcsin ( 12 / 13 ) + arccos ( 4 / 5 ) = arcsin ( k )
Use the compound angle formula sin ( x + y ) = sin ( x ) cos ( y ) + cos ( x ) sin ( y ) to find the exact value of k

Answer & Explanation

Falpo359

Falpo359

Beginner2022-11-20Added 15 answers

If
arcsin 12 13 = x sin x = 12 / 13 , cos x = 1 ( 12 / 13 ) 2 = 5 / 13
and
arccos 4 5 = y cos y = 4 / 5 , sin y = 1 ( 4 / 5 ) 2 = 3 / 5
then
sin ( x + y ) = sin x cos y + sin y cos x = 12 13 4 5 + 5 13 3 5 = 63 65
then
arcsin sin ( x + y ) = arcsin sin 63 65 = arcsin k
k = 63 65

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