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What is the relation ship between sin x and sin (180 - x)? between sin x and sin (180 + x)?

Answer 1

Josiah Anderson

Supplementary arcs:
sin x = sin (180 - x) = #sin (pi - x)#
sin x = - sin (180 + x) = -#sin (pi + x)#

On the trig unit circle,

#sin (pi - x)# = sin (180 - x) = sin x

#sin (pi + x)# = sin (180 + x) = - sin x

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Answer 2

Charles Autterson

The relationships between sin x and sin (180 - x), as well as sin x and sin (180 + x), are as follows:

For sin x and sin (180 - x):
- sin (180 - x) = sin (180)cos(x) - cos(180)sin(x)
- Since sin(180) = 0 and cos(180) = -1, the equation simplifies to: sin (180 - x) = 0*cos(x) - (-1)*sin(x)
- Which further simplifies to: sin (180 - x) = sin(x)
For sin x and sin (180 + x):
- sin (180 + x) = sin (180)cos(x) + cos(180)sin(x)
- Since sin(180) = 0 and cos(180) = -1, the equation simplifies to: sin (180 + x) = 0*cos(x) + (-1)*sin(x)
- Which further simplifies to: sin (180 + x) = -sin(x)

So, the relationship between sin x and sin (180 - x) is sin (180 - x) = sin(x), and the relationship between sin x and sin (180 + x) is sin (180 + x) = -sin(x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.