Sure, let's go through these questions step-by-step:
### Question 2: Convert [tex]\(72^{\circ}\)[/tex] into radians.
To convert degrees to radians, we use the formula:
[tex]\[ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) \][/tex]
So, for [tex]\(72^{\circ}\)[/tex]:
[tex]\[ \text{radians} = 72 \times \left( \frac{\pi}{180} \right) \][/tex]
Simplifying this, we get:
[tex]\[ \text{radians} \approx 72 \times 0.0174533 \][/tex]
This results in:
[tex]\[ \text{radians} \approx 1.2566370614359172 \][/tex]
So, [tex]\(72^{\circ}\)[/tex] is approximately [tex]\(1.257\)[/tex] radians.
### Question 3: If [tex]\(\sec \theta=\frac{5}{4}\)[/tex], then find the value of [tex]\(\cos \theta\)[/tex].
The secant function is the reciprocal of the cosine function. That is:
[tex]\[ \sec \theta = \frac{1}{\cos \theta} \][/tex]
Given:
[tex]\[ \sec \theta = \frac{5}{4} \][/tex]
We can find [tex]\(\cos \theta\)[/tex] by taking the reciprocal of [tex]\(\sec \theta\)[/tex]:
[tex]\[ \cos \theta = \frac{1}{\sec \theta} \][/tex]
So:
[tex]\[ \cos \theta = \frac{1}{\frac{5}{4}} \][/tex]
[tex]\[ \cos \theta = \frac{4}{5} \][/tex]
Simplifying this, we get:
[tex]\[ \cos \theta = 0.8 \][/tex]
Therefore, if [tex]\(\sec \theta = \frac{5}{4}\)[/tex], the value of [tex]\(\cos \theta\)[/tex] is [tex]\(0.8\)[/tex].
