Given a right triangle where the side adjacent to angle $\theta$ is $4$ units and the hypotenuse is $5$ units, what is the value of $\sec \theta$?

• A. $\frac{5}{4}$
• B. $\frac{4}{5}$
• C. $1$
• D. $0$

Answer: (A)

Verified step by step guidance

1. Identify the given elements in the right triangle: the side adjacent to angle \( \theta \) is 4 units, and the hypotenuse is 5 units.
2. Recall the definition of secant in terms of cosine: \( \sec(\theta) = \frac{1}{\cos(\theta)} \).
3. Express cosine of angle \( \theta \) using the adjacent side and hypotenuse: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{5} \).
4. Calculate secant by taking the reciprocal of cosine: \( \sec(\theta) = \frac{1}{\cos(\theta)} = \frac{1}{\frac{4}{5}} \).
5. Simplify the expression for secant: \( \sec(\theta) = \frac{5}{4} \).