Question

a point on the terminal side of an angle θ in standard position is (-2, -6). find the exact value of each of the six trigonometric functions of θ
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression )
b. the function is not defined.
select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. cscθ = -√10/3
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression )
b. the function is not defined.
select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. secθ = -√10
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression )
b. the function is not defined.
select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. cotθ =

Explanation:

Step1: Calculate the radius \(r\)

For a point \((x,y)=(-2,-6)\) on the terminal side of an angle \(\theta\) in standard position, use the formula \(r = \sqrt{x^{2}+y^{2}}\).

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Step2: Recall the definition of \(\cot\theta\)

The cotangent function is defined as \(\cot\theta=\frac{x}{y}\) (where \(x=-2\) and \(y = - 6\)).

$$ \cot\theta=\frac{-2}{-6}=\frac{1}{3} $$

Answer:

\(\cot\theta=\frac{1}{3}\)