Question

Need help finding the exact value of sec pi/3

Answer 1

The exact value of sec(pi/3) is 2.

Step-by-step explanation:

The question asks for the exact value of sec(pi/3).

We know that the secant function is the reciprocal of the cosine function.

To find the exact value of cos(pi/3), we can use the unit circle.

1. Start by drawing a circle with a radius of 1 unit.
2. Divide the circle into six equal parts.
3. The angle pi/3 corresponds to one of these parts.
4. At this angle, the x-coordinate of the point on the unit circle is 1/2 and the y-coordinate is sqrt(3)/2.
5. The cosine function is defined as the x-coordinate, so cos(pi/3) = 1/2.

Now, since sec(x) = 1/cos(x), we can find the value of sec(pi/3) by taking the reciprocal of cos(pi/3). Therefore, sec(pi/3) = 1/(1/2) = 2.

Answer 2

Given:

`sec((\pi)/(3))`

To find the exact value,

Step 1: Apply the trigonometri identieties.

From the trigonometric identities,

`sec\text{ }\theta\text{ =}(1)/(cos\theta)`

This implies that

`sec((\pi)/(3))=(1)/(\cos((\pi)/(3)))`

Step 2: Evaluate the exact value.

`\begin{gathered} since \\ \cos((\pi)/(3))=(1)/(2), \\ we\text{ have} \\ sec((\pi)/(3))=(1)/(\cos(\pi\/3))=(1)/((1)/(2))=2 \end{gathered}`

Hence, te exact value of

`sec((\pi)/(3))`

is evaluated to be 2