Diketahui sin A = 3/5 dan cos B =8/17 , < A sudut lancip dan < p sudut tumpul . Hitunglah nilai dari A. Sin ( A + B )
Pandanwangi
<A lancip. <B tumpul sin A = 3/5 --> cos A = 4/5 cos B = - 8/17 --> sin B = 15/17 . sin (A+B) = sin A cos B + cos A sinB = (3/5)(-8/17) + (4/5)(15/17) = ( -24+ 60)/(85) = 36/85
Pandanwangi
salah satu cara nya pake rumus sin² x + cos² x = 1
sin A = 3/5 --> cos² A = 1 - sin² A = 1 - 3/5² = 1 - 9/25
cos² A = 16/25
cos A = 4/5 atau cos A = - 4/5
krn A lancip maka cos A = 4/5 ( positif)
sin A = 3/5 --> cos A = 4/5
cos B = - 8/17 --> sin B = 15/17
.
sin (A+B) = sin A cos B + cos A sinB
= (3/5)(-8/17) + (4/5)(15/17)
= ( -24+ 60)/(85)
= 36/85