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Nezavi [6.7K]
3 years ago
13

Can someone help me with this question lol, i’ll mark as brainliest if correct

Mathematics
2 answers:
maw [93]3 years ago
5 0

Answer:

The answer would be number 3, I hope this helps. Let me know of you need an explanation.

andriy [413]3 years ago
5 0

Hi there! Before we start with your problem. Recall the Trigonometric Function of (-x) first.

  • sin(-x) = -sinx
  • cos(-x) = cosx
  • tan(-x) = -tanx

Now what we need to do is to imagine a unit circle. We know that angle (-x) rotate clockwise while (x) rotates counterclockwise.

Now imagine if it rotates clockwise, it:d start at the fourth quadrant first. That means the y-value is negative while x-value is positive.

We also know that (x, y) = (cos, sin)

Now move to the 2(pi)/3.

\large{ \frac{2 \pi}{ 3}  =  \frac{2(180)}{3}  \longrightarrow  2(60)=  \boxed{120 \degree}}

Thus, the value of 2pi/3 is 120°

Now imagine again. In a unit circle, 120° is in second quadrant if we rotate counterclockwise. But if we rotate clockwise, where would the 120° be? Remember that (-x) rotates clockwise. That's right! (-120°) is in the third quadrant. In the third quadrant, cos is negative there along with sin.

So we can conclude that:

  • cos(-120°) is in third quadrant.
  • cos and sin are negative in third quadrant.

120° is also a reference angle of 60° because of 180°-60° = 120°

Thus,

\large{cos( -  \frac{2 \pi}{3}  )= cos( - 120 \degree)  = cos(120 \degree) \longrightarrow  -  \frac{1}{2} }

Answer/Conclusions

  • cos(-2pi/3) = -1/2
  • cos(-2pi/3) use the reference of 60°
  • cos(-2pi/3) is in third quadrant.
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