Question

trigonometric functions question 2, 3.2.2 points: 0 of 4 the terminal side of an angle θ in standard position passes through the point (-6, -2) use the figure to find the following value. sinθ sinθ = (type an exact answer in simplified form. rationalize all denominators.)

Explanation:

Step1: Identify x, y, r

Given point \((-6, -2)\), so \(x = -6\), \(y = -2\). Calculate \(r\) (distance from origin) using \(r = \sqrt{x^2 + y^2}\).
\(r = \sqrt{(-6)^2 + (-2)^2} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10}\)

Step2: Apply sine formula

Sine of \(\theta\) is \(\sin\theta = \frac{y}{r}\). Substitute \(y = -2\) and \(r = 2\sqrt{10}\).
\(\sin\theta = \frac{-2}{2\sqrt{10}} = \frac{-1}{\sqrt{10}}\)

Step3: Rationalize denominator

Multiply numerator and denominator by \(\sqrt{10}\): \(\frac{-1 \times \sqrt{10}}{\sqrt{10} \times \sqrt{10}} = \frac{-\sqrt{10}}{10}\)

Answer:

\(-\frac{\sqrt{10}}{10}\)