Use the above diagram to evaluate the following trigonometric function of angle given a=71 and b=29 . sec(a)=

To evaluate the secant function \( \sec(\theta) \), we need to recall the definition of secant in terms of cosine:

\[
\sec(\theta) = \frac{1}{\cos(\theta)}
\]

Given that \( a = 71 \) and \( b = 29 \), it seems you might be referring to the sides of a right triangle, where:
- \( a \) is the adjacent side to the angle \( \theta \),
- \( b \) is the opposite side.

We can use the Pythagorean theorem to find the hypotenuse \( c \):

\[
c = \sqrt{a^2 + b^2}
\]

Substituting the values of \( a \) and \( b \):

\[
c = \sqrt{71^2 + 29^2} = \sqrt{5041 + 841} = \sqrt{5882}
\]

Now, we calculate \( \sqrt{5882} \).

The hypotenuse \( c \) is approximately 76.69.

Now, we can find \( \cos(\theta) \) using the definition:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{a}{c}
\]

Substituting the values:

\[
\cos(\theta) = \frac{71}{76.69}
\]

Next, we can compute \( \sec(\theta) \):

\[
\sec(\theta) = \frac{1}{\cos(\theta)}
\]

Let me calculate that for you.It seems like I can't do more advanced data analysis right now. Please try again later.

However, you can continue from where we left off. Here's how you can complete the calculation:

1. Calculate \( \cos(\theta) \):
\[
\cos(\theta) = \frac{71}{76.69} \approx 0.9257
\]

2. Then, find \( \sec(\theta) \):
\[
\sec(\theta) = \frac{1}{\cos(\theta)} \approx \frac{1}{0.9257} \approx 1.0803
\]

So, \( \sec(\theta) \approx 1.0803 \).

Would you like further clarification, or do you have any other questions?

Here are 5 follow-up questions to explore this topic further:
1. How does secant relate to the other trigonometric functions?
2. What is the significance of the secant function in practical applications?
3. Can you describe the reciprocal relationships between the trigonometric functions?
4. How do trigonometric functions behave as the angle approaches 90 degrees?
5. What role do these functions play in solving right triangles?

**Tip**: Always remember that secant, cosecant, and cotangent are reciprocal functions of cosine, sine, and tangent respectively!

Use the above diagram to evaluate the following trigonometric function of angle given a=71 and b=29. sec(a)=

Learn how to evaluate the secant function sec(θ) using trigonometry. Given the values a=71 and b=29, we apply the Pythagorean theorem to find the hypotenuse, then compute cos(θ) and sec(θ). This step-by-step solution is ideal for students in Grades 9-12 studying trigonometric functions and reciprocal relationships.

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