Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

[tex]\[
\begin{array}{l}
\sec \theta=\frac{1}{\cos \theta}=\frac{1}{-\frac{5 \sqrt{26}}{26}}=\frac{-\sqrt{26}}{5} \\
\cot \theta=\frac{1}{\tan \theta}=\frac{1}{\frac{1}{5}}=5
\end{array}
\][/tex]

Which of the following explains whether all of Francesca's work is correct?

A. Each step is correct because she plotted the point, drew a line to the [tex]\( x \)[/tex]-axis to form a right triangle, used the Pythagorean theorem to find the hypotenuse, and finally wrote the correct ratios for all six functions.

B. She made her first error in step 1 because she should have drawn the line to the [tex]\( y \)[/tex]-axis to form the right triangle.

C. She made her first error in step 2 because she should have used a negative value for [tex]\( \cos \theta \)[/tex].

D. She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and cotangent functions.

Sagot :

GinnyAnswer
To determine where Francesca made her first error, let's carefully analyze the problem step-by-step:

1. Evaluate [tex]\( \sec \theta = \frac{1}{\cos \theta} \)[/tex]:
- Given as [tex]\( \frac{1}{-\frac{5 \sqrt{26}}{26}} \)[/tex].
- Upon simplifying: [tex]\( \frac{1}{-\frac{5 \sqrt{26}}{26}} = \frac{26}{-5 \sqrt{26}} \)[/tex].
- Further simplification should yield: [tex]\( \frac{26}{-5 \sqrt{26}} = \frac{-26}{5 \sqrt{26}} = - \frac{\sqrt{26}}{5} \)[/tex], not [tex]\( \frac{-\sqrt{2b}}{5} \)[/tex].

2. Evaluate [tex]\( \cot \theta = \frac{1}{\tan \theta} \)[/tex]:
- Given as [tex]\( \frac{1}{\frac{1}{5}} = 5 \)[/tex], which is correctly simplified.

From the above steps, it's clear where the errors and incorrect simplifications occurred. Specifically:

- In Step 1, Francesca simplified [tex]\(\sec \theta\)[/tex] incorrectly, mixing up the expression and resulting in a wrong ratio.

Therefore, the correct explanation is:
She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.

Thus, the correct answer is:
She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.