Question

a triangle is graphed on the unit circle as shown.
what is the value of \\(\sin(\theta)\\) for the triangle where \\(\theta\\) is the labeled angle? round decimal answers to the nearest hundredth.
\\(\circ\\) a. \\(1.41\\)
\\(\circ\\) b. \\(1\\)
\\(\circ\\) c. \\(0.71\\)
\\(\circ\\) d. \\(-0.71\\)

Explanation:

Step1: Recall the definition of sine in the unit circle

For a point \((x,y)\) on the unit circle corresponding to an angle \(\theta\), \(\sin(\theta)=y\).

Step2: Identify the \(y\) - coordinate of the given point

The given point is \((\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})\). The \(y\) - coordinate is \(-\frac{\sqrt{2}}{2}\).

Step3: Calculate the decimal value of \(-\frac{\sqrt{2}}{2}\)

We know that \(\sqrt{2}\approx1.414\), so \(-\frac{\sqrt{2}}{2}\approx-\frac{1.414}{2}=- 0.707\approx - 0.71\)

Answer:

D. - 0.71