Question

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

Answer 1

Answer:

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

Answer 2

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.