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
select the correct choice and, if necessary, fill in the answer box to complete your choice
a. sinθ=
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression)
b. the function is not defined

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 \(r = \sqrt{x^{2}+y^{2}}\).

$$
LATEXBLOCK0
$$

Step2: Calculate \(\sin\theta\)

Use the formula \(\sin\theta=\frac{y}{r}\). Here \(y=-6\) and \(r = 2\sqrt{10}\).

$$
LATEXBLOCK1
$$

Answer:

\(\sin\theta=-\frac{3\sqrt{10}}{10}\)