Trig question: transformation (1 Viewer)

[mrman]

can someone find the exact value of

sinx-cosx=1

-pi<(or equal to)x<(or equal to)pi


The problem is I dont exactly know what to do, with negative pi, and what valuews of x u get with that.

I know im pretty screwed half yearly in like 5 days lol!!!!!


NOOOOOOOOOOO

 

[kini mini]

Originally posted by mrman

The problem is I dont exactly know what to do, with negative pi, and what valuews of x u get with that.

In that case, I'll give you clues rather than tell you what to do...

A clue...that indicates the domain in which you have to find solutions .

Another clue: sketch the y= sin x and y = cos x graphs on the same axes for the given domain, and see if you understand the question any better

Then see if you can solve algebraically .

 

[chunder]

what you do is express sinx-cox=1 in the form of rsin(x-a)=1

i.e. let sinx-cosx=rsinxcosa-rcosxsina=1

by equating: rcosa=1 and rsina=1

therefore r = root 2
in addition since tan a=1, a=45

therefore sinx-cosx=(root 2)sin(x-45)=1

etc etc etc

your answers will be 90 and 180

 

[wogboy]

Alternatively, you can square both sides to get the solutions.

sinx - cosx = 1

sin^2x - 2sinxcosx + cos^2x = 1

1 - 2sinxcosx = 1

2sinxcosx = 0

sinx = 0 or cosx = 0 (or if you like, you can say sin2x = 0)

so the possibilities for x are:

x = pi
x = 0
x = -pi
x = pi/2
x = -pi/2

now because we squared both sides of the equation initially, you have to verify each answer (otherwise we can prove -1 = 1 )

sin(pi) - cos(pi) = 1, so x = pi is true.
sin(0) - cos(0) = -1, so x = 0 is false.
sin(-pi) - cos(-pi) = 1, so x = -pi is true.
sin(pi/2) - cos(pi/2) = 1, so x = pi/2 is true.
sin(-pi/2) - cos(-pi/2) = -1, so x = -pi is false.

so the final solutions are,

x = pi, x = -pi, x = pi/2

 

[mrman]

Now i get it

Thanks heaps wogboy, Now I get it. Lol kini mini, I know what you do with the domain, but it was a bit hazy because in the worked solutions they said -5pi/4 and Im like perhaps im retarded and dont know what a domain is lol. But thanks all of you guys for helping....


much obliged

 

[kini mini]

Originally posted by chunder
your answers will be 90 and 180

If the question is framed in radians, then you must answer in radians. What about the negative solutions? I did like wogboy, except I shifted cos x to the RHS and had it all in terms of cos .

mrman , where does -5pi/4 come from ?

 

[mrman]

ohok thanks... now i getcha

thanks for helping