KRLoopy7940 KRLoopy7940
  • 21-10-2019
  • Mathematics
contestada

If theta = n ∙ 360 + 180, for some integer n, then cos(theta°) = _____, and sin(theta°) = ______.

Respuesta :

ConcepcionPetillo ConcepcionPetillo
  • 24-10-2019

Answer:

- 1, 0

Solution:

As per the question:

[tex]\theta = 360n + 180^{\circ}[/tex]

Now,

We know that:

[tex]cos(2\pi n + \phi) = cos\phi[/tex]

Also,

[tex]sin(2\pi n + \phi) = cos\phi[/tex]

In the question, [tex]\phi = 180^{\circ}[/tex]

Therefore, we can write:

[tex]cos(360n + 180^{\circ}) = cos180^{\circ}[/tex]

We know that:

[tex]cos180^{\circ} = - 1[/tex]

Similarly,

[tex]sin(360n + 180^{\circ}) = sin180^{\circ}[/tex]

We know that:

[tex]cos180^{\circ} = 0[/tex]

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