Could you simplify sin(360⁰-θ)?

[Indranil]

Could you please simplify sin(360⁰-θ)? what does it mean? I don't understand it.

 

[MarkFL]

The period of the sine function in degrees is \(\displaystyle 360^{\circ}\), thus:

\(\displaystyle \sin(360^{\circ}-\theta)=\sin(-\theta+360^{\circ})=\sin(-\theta)\)

The sine function is odd, thus:

\(\displaystyle \sin(-\theta)=-\sin(\theta)\)

And so we conclude:

\(\displaystyle \sin(360^{\circ}-\theta)=-\sin(\theta)\)

 

[Indranil]

The period of the sine function in degrees is \(\displaystyle 360^{\circ}\), thus:

\(\displaystyle \sin(360^{\circ}-\theta)=\sin(-\theta+360^{\circ})=\sin(-\theta)\)

The sine function is odd, thus:

\(\displaystyle \sin(-\theta)=-\sin(\theta)\)

And so we conclude:

\(\displaystyle \sin(360^{\circ}-\theta)=-\sin(\theta)\)

'The period of the sine function in degrees is \(\displaystyle 360^{\circ}\), thus:

\(\displaystyle \sin(360^{\circ}-\theta)=\sin(-\theta+360^{\circ})=\sin(-\theta)\)'
I don't understand it. Could you please simplify it a little bit so that I can understand?

 

[mmm4444bot]

\(\displaystyle \sin(360^{\circ}-\theta)=\sin(-\theta+360^{\circ})=\sin(-\theta)\)

I don't understand it. Could you please [find a way to explain it] so that I can understand?

Please tell us which part confuses you. I don't know what it is that you don't understand.

The algebra? The function notation? The concept of 'period'? The meaning of 'identity'?

360° - θ = -θ + 360° (that's algebra)

The expression -θ + 360° means the measurement -θ has been increased by 360°.

If we increase sine's input by 360°, we get the same output because the sine function repeats its behavior every 360° (that's the period).

sin(-θ + 360°) = sin(-θ)

This equation is true for any value of θ, so it's an identity.

Input the number -θ, and the sine function outputs the number sin(-θ).

Now increase the input by 360°, and the sine function outputs the same number sin(-θ).

sin(-θ) = sin(-θ + 360°)