Solve for x? 1-sin^2 x=(0.728-0.44sinx)^2

badlife18va

badlife18va

Answered question

2022-08-04

Solve for x?
1 sin 2 x = ( 0.728 0.44 sin x ) 2

Answer & Explanation

Jaelyn Rosario

Jaelyn Rosario

Beginner2022-08-05Added 16 answers

let sin x = a
so, 1 sin 2 x = ( 0.728 0.44 sin x ) 2
1 a 2 = ( 0.728 0.44 a ) 2
1 a 2 = ( 0.728 ) 2 + ( 0.44 a ) 2 2 0.728 0.44 a
1 a 2 = 0.53 + 0.194 a 2 0.64 a
0.53 1 + 0.194 a 2 + a 2 0.64 a = 0
1.194 a 2 0.64 a 0.47 = 0
a = [ ( 0.64 ) ± 0.64 2 4 1.194 ( 0.47 ) ] / 2 1.194
= [ 0.64 ± 2.65 ] / 2.39
= [ 0.64 ± 1.63 ] / 2.39
hence a = 0.948 or a = - 0.414
hence sin x = 0.948 or sin x = 0.414
x = sin 1 ( .948 ) or x = sin 1 ( 0.414 )
= 71.442 or = 24.456
Answer: x = 71.442 or x = 24.456

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