sin(x)+sin(π-x)=?

Question

what is the answer and how do you get it?

square root of 1-(x squared) the same as sin(x)+cos(x)?

Answer 1

sinx + sinπcosx - cosπsinx
= 2sinx

In case you're having problems getting sinπ = 0, you need to change to the radian mode in your calculator.

Answer 2

Not quite CPUcate.
sin(π-x) is actually just equal to sin(x).
Have a look at a sine wave: at x=zero going right it is going up and at x=180 degrees (i.e. π) going left it is also going up.
Alternatively sin(x) has mirror reflectivity about its apex π/2. so sin(π/2-y)=sin(π/2+y), substitute y=π/2-x gives sin(x)=sin(π-x)
therefore:
sin(x)+sin(π-x)=2sin(x)

As for the additional comment:
sinx+cosx=sqrt(1-x^2)
this is not true
square both sides:
sin^2(x)+cos^2(x)+2sin(x)cos(x)=1-x^2
1+2sin(x)cos(x)=1-x^2
sin(2x)=-x^2
substitute x=π
sin(2x)=0 which does not = -π^2
or more quickly you can see its not true because when x>1 the right hand side will be square root of a negative number whereas the left hand side there are no problems like that.

Answer 3

sin(x) and sin(pi -x) have the same value...

so sin(x) + sin(pi - x) = 2sin(x)

A bit more explanation (assuming you know a little trig):

Sin is positive in the first and second quadrant. The value of the sine of an angle is based on the reference angle. The reference angle is found by subtracting the angle from pi.

For example, an angle of 3pi/4 (135 deg) has a reference angle of pi/4 (45 deg) because pi - 3pi/4 = pi/4.

So, if x = pi/4 ....then pi - x = 3pi/4

The reference angles are the same, and one angle is in the first quadrant and the other is in the second quadrant, so the value of sine for each angle is the same.

I hope this wasn't too confusing...

Answer 4

= sin x + sin x
= 2 sin x
Note
sin (π - x) is in 2nd quadrant is +ve and = sin x

Answer 5

You will use a double angle formula:
sin(A-B) = sinAcosB - cosAsinB

sin(x) + sin(pi - x) = sin(x) + [sin(pi)cos(x) - cos(pi)sin(x)]

sin(pi) = 0 and cos(pi) = -1 so now you get:
sin(x) + 0*cos(-x) + sin(x) = sin(x) + sin(x) = 2sin(x).

Answer 6

let y = sin x + sin (pi - x)

since sin (pi - x) = cos x

y = sin x + cos x

Answer 7

sin(x) + sin(pi - x)
sin(x) + sin(pi)cos(x) - sin(x)cos(pi)
sin(x) + 0cos(x) - (-1)sin(x)
sin(x) + sin(x)
2sin(x)

sin(x) + sin(pi - x) = 2sin(x)