Question

What is the value of sec theta given the diagram below?

Answer 1

Answer:

$\sec \theta=-\sqrt{5}$

Step-by-step explanation:

The hypotenuse is $h^2=6^2+3^2$

$h^2=36+9$

$h^2=45$

$h=\sqrt{45}$

$h=3\sqrt{5}$

The terminal side of $\theta$ is in the second quadrant.

In this quadrant; the secant ratio is negative.

$\sec \theta=-\frac{hypotenuse}{adjacent}$

$\sec \theta=-\frac{3\sqrt{5}}{3}$

$\sec \theta=-\sqrt{5}$

Answer 2

The value of sec theta is $\sec(\theta) = -\sqrt5$

How to determine the value of sec theta

From the diagram, we start by calculating the length of the hypotenuse (h).

So, we have:

$h = \sqrt{6^2 + 3^2$

Evaluate

$h = \sqrt{45$

Simplify

$h = 3\sqrt{5$

The value of the secant in the second quadrant is calculated as:

$\sec(\theta) = -\frac{Hypotenuse}{Adjacent}$

So, we have:

$\sec(\theta) = -\frac{3\sqrt5}{3}$

Evaluate

$\sec(\theta) = -\sqrt5$

Hence, the value of sec theta is $\sec(\theta) = -\sqrt5$

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