Question

sketch an angle θ in standard position such that θ has the least possible positive measure and the point (6,8) is on the terminal side of θ. then find the exact values of the six trigonometric functions for θ.

b. the function is undefined.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a.
tan θ = \frac{4}{3} (simplify your answer. type an integer or a fraction.)
b. the function is undefined.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a.
csc θ = \frac{5}{4} (simplify your answer. type an integer or a fraction.)
b. the function is undefined.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a.
sec θ = \frac{5}{3} (simplify your answer. type an integer or a fraction.)
b. the function is undefined.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. cot θ = \square (simplify your answer. type an integer or a fraction.)
b. the function is undefined.

Explanation:

Step1: Recall the definition of cotangent

The cotangent of an angle \(\theta\) in standard position with a point \((x,y)\) on the terminal side is defined as \(\cot\theta=\frac{x}{y}\), where \(x\) and \(y\) are the coordinates of the point, and \(y
eq0\).

Step2: Identify \(x\) and \(y\) from the point \((6,8)\)

For the point \((6,8)\), we have \(x = 6\) and \(y=8\).

Step3: Calculate \(\cot\theta\)

Using the formula \(\cot\theta=\frac{x}{y}\), substitute \(x = 6\) and \(y = 8\). So \(\cot\theta=\frac{6}{8}\), which simplifies to \(\frac{3}{4}\) (by dividing both the numerator and the denominator by their greatest common divisor, which is 2).

Answer:

\(\frac{3}{4}\)