[F. 3 Maths] Trigonometric Relations (Only 3 questions!)
Solve for x in the following equations.
1. sin ( 4x + 60' ) = cos 6x
2. sin ( 3x + 11' ) = cos ( 2x - 6' )
3. 1/(tan 4x) = (sin 5x)/(cos 5x)
Remarks: 1. ' = degree(s) 2. / = over
[F. 3 Maths] Trigonometric Relations (Only 3 questions!)
2007-05-25 6:21 am
回答 (2)
2007-05-25 8:49 am
✔ 最佳答案
1. sin ( 4x + 60' ) = cos 6x=cos [90-(4x+60)] = cos 6x
Therefore
[90-(4x+60)] = 6x
90-4x-60 = 6x
30-4x = 6x
30 = 10x
x = 3
2. sin ( 3x + 11' ) = cos ( 2x - 6' )
=cos[90- (3x+11)] = cos(2x-6)
Therefore
90- (3x+11)= 2x-6
90-3x-11 = 2x-6
79-3x = 2x-6
79+6 = 2x+3x
85 = 5x
x =17
3. 1/(tan 4x) = (sin 5x)/(cos 5x)
= tan (90-4x)= tan 5x
Therefore
90-4x= 5x
90 = 9x
x =10
2007-05-25 6:27 am
1. sin ( 4x + 60' ) = cos 6x
cos (90 - 4x+60')=cos 6x
90- 4x-60=6x
10x=30
x=3
2. sin ( 3x + 11' ) = cos ( 2x - 6' )
cos (90-3x+11')=cos ( 2x - 6' )
90-3x-11'=2x-6'
5x=85
x=17
3. 1/(tan 4x) = (sin 5x)/(cos 5x)
1/tan4x=tan5x
tan(90-4x)=tan 5x
90-4x=5x
9x=90
x=10'
cos (90 - 4x+60')=cos 6x
90- 4x-60=6x
10x=30
x=3
2. sin ( 3x + 11' ) = cos ( 2x - 6' )
cos (90-3x+11')=cos ( 2x - 6' )
90-3x-11'=2x-6'
5x=85
x=17
3. 1/(tan 4x) = (sin 5x)/(cos 5x)
1/tan4x=tan5x
tan(90-4x)=tan 5x
90-4x=5x
9x=90
x=10'
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