Does #sin180+sin45=sin225#?

2 Answers
Nov 25, 2016

Answer:

Ehm...I do not think so...

Explanation:

I imagine the arguments in degrees so that if you plot your sin function you get:
enter image source here
As you can see:
#sin(180^@)=0#
while #sin(45^@)# is positive and #sin(225^@)# is negative.

I also considered the possibility to have them in radians but it doesn't work either...

Nov 25, 2016

Answer:

No

Explanation:

Remember that taking the #sin# of something is a function that is unique only to that number (let's imagine that we're in a range of #0< theta < 2pi#).

So the #sin 180# is a certain value and the #sin45# is a certain value. The #sin 225# is also a separate certain value. You cannot find the #sin# of two different values, and add them up to be the #sin# of their sum.

Think of it this way:

#sqrt4 + sqrt25 = sqrt29#
#2+5=sqrt29#
#7cancel(=)sqrt29#

In the same idea, #sin# does not work that way.

Like Gio explained, the graphs are also different.

But how can you trust just plain words? Let's actually work out this problem.

#sin180# = 0

#sin(45) = sqrt2/2#

#sin225 = -sqrt2/2#

So:

#sin180 + sin45 = sin225#

#0 + sqrt2/2 cancel(=) -sqrt2/2#

And that's why you cant work with #sin# like that!