QuestionCalculate $(-4) \cos \left(\frac{2 \pi}{3}\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $(-4) \cos \left(\frac{ \pi}{3}\right)$ . We are using the standard mathematical convention where $\cos$ is the cosine function and $\pi$ is the mathematical constant Pi, approximately equal to3.141593. We are assuming the angle is in radians, not degrees

STEP 2

First, we need to evaluate the cosine of the angle $\frac{2 \pi}{}$ .
$\cos \left(\frac{2 \pi}{}\right)$

STEP 3

The cosine of $\frac{2 \pi}{3}$ is equivalent to the cosine of120 degrees, which is $-0.5$ .
$\cos \left(\frac{2 \pi}{3}\right) = -0.5$

STEP 4

Now that we have the value of the cosine, we can multiply this by $-4$ .
$-4 \times \cos \left(\frac{2 \pi}{3}\right)$

STEP 5

Plug in the value of $\cos \left(\frac{2 \pi}{3}\right)$ to calculate the result.
$-4 \times -0.5$

STEP 6

Calculate the result.
$-4 \times -0.5 =2$ The result of $(-4) \cos \left(\frac{2 \pi}{3}\right)$ is2.

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QuestionCalculate $(-4) \cos \left(\frac{2 \pi}{3}\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $(-4) \cos \left(\frac{ \pi}{3}\right)$ . We are using the standard mathematical convention where $\cos$ is the cosine function and $\pi$ is the mathematical constant Pi, approximately equal to3.141593. We are assuming the angle is in radians, not degrees

STEP 2

First, we need to evaluate the cosine of the angle $\frac{2 \pi}{}$ .
$\cos \left(\frac{2 \pi}{}\right)$

STEP 3

The cosine of $\frac{2 \pi}{3}$ is equivalent to the cosine of120 degrees, which is $-0.5$ .
$\cos \left(\frac{2 \pi}{3}\right) = -0.5$

STEP 4

Now that we have the value of the cosine, we can multiply this by $-4$ .
$-4 \times \cos \left(\frac{2 \pi}{3}\right)$

STEP 5

Plug in the value of $\cos \left(\frac{2 \pi}{3}\right)$ to calculate the result.
$-4 \times -0.5$

STEP 6

Calculate the result.
$-4 \times -0.5 =2$ The result of $(-4) \cos \left(\frac{2 \pi}{3}\right)$ is2.

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QuestionCalculate (−4)cos⁡(2π3)(-4) \cos \left(\frac{2 \pi}{3}\right)(−4)cos(32π​).

Studdy Solution

STEP 1

STEP 2

First, we need to evaluate the cosine of the angle 2π\frac{2 \pi}{}2π​.cos⁡(2π)\cos \left(\frac{2 \pi}{}\right)cos(2π​)

STEP 3

The cosine of 2π3\frac{2 \pi}{3}32π​ is equivalent to the cosine of120 degrees, which is −0.5-0.5−0.5.cos⁡(2π3)=−0.5\cos \left(\frac{2 \pi}{3}\right) = -0.5cos(32π​)=−0.5

STEP 4

Now that we have the value of the cosine, we can multiply this by −4-4−4.−4×cos⁡(2π3)-4 \times \cos \left(\frac{2 \pi}{3}\right)−4×cos(32π​)

STEP 5

Plug in the value of cos⁡(2π3)\cos \left(\frac{2 \pi}{3}\right)cos(32π​) to calculate the result.−4×−0.5-4 \times -0.5−4×−0.5

STEP 6

Calculate the result.−4×−0.5=2-4 \times -0.5 =2−4×−0.5=2The result of (−4)cos⁡(2π3)(-4) \cos \left(\frac{2 \pi}{3}\right)(−4)cos(32π​) is2.

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QuestionCalculate $(-4) \cos \left(\frac{2 \pi}{3}\right)$ .

First, we need to evaluate the cosine of the angle $\frac{2 \pi}{}$ .
$\cos \left(\frac{2 \pi}{}\right)$

The cosine of $\frac{2 \pi}{3}$ is equivalent to the cosine of120 degrees, which is $-0.5$ .
$\cos \left(\frac{2 \pi}{3}\right) = -0.5$

Now that we have the value of the cosine, we can multiply this by $-4$ .
$-4 \times \cos \left(\frac{2 \pi}{3}\right)$

Plug in the value of $\cos \left(\frac{2 \pi}{3}\right)$ to calculate the result.
$-4 \times -0.5$

Calculate the result.
$-4 \times -0.5 =2$ The result of $(-4) \cos \left(\frac{2 \pi}{3}\right)$ is2.