# HOW TO SOLVE SIN5X =

And at 3pi/8 + n(pi/4).....however the previous solution covers this one as well....so we have.......pi/8 + n(pi/4)

Here"s the graph of the intersection points < in degrees>.......https://www.desmos.com/calculator/jv5zqyexum

CPhill Dec 4, 2015
edited byCPhill Dec 5, 2015edited byCPhill Dec 5, 2015

#1 +495
+15

sin(5x) = sin(3x)

general solution in radians:

x = 0 + πn

x=π/8 + πn/4

LambLamb Dec 4, 2015
edited byLambLamb Dec 4, 2015
#2 +117737
+10

Good work LambLamb,

I got exactly the same answer.

Bạn đang xem: How to solve sin5x =

But

are you going to show how you did it?

Melody Dec 4, 2015
#3 +124525
+15

sin(3x) = sin(4x -x ) = sin4xcosx - sinxcos4x

sin(5x) = sin(4x + x) = sin4xcosx + sinxcos4x .......so....

sin4xcosx + sinxcos4x = sin4xcosx - sinxcos4x

2sinxcos4x = 0 divide both sides by 2

sinxcos4x = 0

So either

sinx = 0 which happens at 0 + nPi where n is an integer

or

cos(4x) = 0

cos(x) = 0 at pi/2 và 3pi/2

So.....dividing each angle by 4 we have that

cos(4x) = 0 at pi/8 + n(pi/4) where n is an integer

And at 3pi/8 + n(pi/4).....however the previous solution covers this one as well....so we have.......pi/8 + n(pi/4)

Here"s the graph of the intersection points < in degrees>.......https://www.desmos.com/calculator/jv5zqyexum

CPhill Dec 4, 2015
edited byCPhill Dec 5, 2015edited byCPhill Dec 5, 2015
#4 +10

Solve for x: sin(5 x) = sin(3 x) Take the inverse sine of both sides: 5 x = pi-3 x+2 pi n_1 for n_1 element Z or 5 x = 3 x+2 pi n_2 for n_2 element Z add 3 x lớn both sides: 8 x = pi+2 pi n_1 for n_1 element Z or 5 x = 3 x+2 pi n_2 for n_2 element Z Divide both sides by 8: x = pi/8+(pi n_1)/4 for n_1 element Z or 5 x = 3 x+2 pi n_2 for n_2 element Z Subtract 3 x from both sides: x = pi/8+(pi n_1)/4 for n_1 element Z or 2 x = 2 pi n_2 for n_2 element Z Divide both sides by 2: Answer: | | x = pi/8+(pi n_1)/4 for n_1 element Z or x = pi n_2 for n_2 element Z

Guest Dec 5, 2015
#5 +117737
+10

sin(5x) = sin(3x)

Thanks LambLamb CPhill và guest #4 I think this answer is probably very similar to lớn guest #4

Melody Dec 5, 2015

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