Find the exact value of each of the remaining trigonometric functions of . Rationalize denominators when applicable.
. given that is in quadrant IV
(Simplty your answer, including any radicals. Use integers or tractuons for any numbers in the expression.)
B. The function is undefined.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
B. The function is undefined.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
B. The function is undefined.

Ask by Summers Barker. in the United States

Mar 13,2025

Question

Find the exact value of each of the remaining trigonometric functions of . Rationalize denominators when applicable.
. given that is in quadrant IV
(Simplty your answer, including any radicals. Use integers or tractuons for any numbers in the expression.)
B. The function is undefined.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
B. The function is undefined.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
B. The function is undefined.

Ask by Summers Barker. in the United States

Mar 13,2025

UpStudy AI · Accepted Answer

To find the remaining trigonometric functions of $$ \theta $$ given that $$ \tan \theta = -\frac{3}{4} $$ and $$ \theta $$ is in quadrant IV, we can follow these steps:

1. **Identify the sides of the triangle**: 
   - Since $$ \tan \theta = \frac{\text{opposite}}{\text{adjacent}} $$, we can let the opposite side be $$ -3 $$ (negative because we are in quadrant IV) and the adjacent side be $$ 4 $$.

2. **Calculate the hypotenuse**:
   - We can use the Pythagorean theorem to find the hypotenuse $$ r $$:
   $$
   r = \sqrt{(-3)^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
   $$

3. **Find the remaining trigonometric functions**:
   - Now we can find the values of $$ \sin \theta $$, $$ \cos \theta $$, $$ \sec \theta $$, and $$ \cot \theta $$:
   - $$ \sin \theta = \frac{\text{opposite}}{r} = \frac{-3}{5} $$
   - $$ \cos \theta = \frac{\text{adjacent}}{r} = \frac{4}{5} $$
   - $$ \sec \theta = \frac{1}{\cos \theta} = \frac{5}{4} $$
   - $$ \cot \theta = \frac{1}{\tan \theta} = \frac{4}{-3} = -\frac{4}{3} $$

Now, let's summarize the results:

- **Secant**:
  $$
  \sec \theta = \frac{5}{4}
  $$

- **Cotangent**:
  $$
  \cot \theta = -\frac{4}{3}
  $$

Thus, the answers are:

A. $$ \sec \theta = \frac{5}{4} $$

A. $$ \cot \theta = -\frac{4}{3} $$
A. $$ \sec \theta = \frac{5}{4} $$ A. $$ \cot \theta = -\frac{4}{3} $$

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