Determine which of the following angles on the unit circle has coordinates \(\left(-\dfrac{1}{\sqrt{2}}, -\dfrac{1}{\sqrt{2}}\right)\).
- \(135^{\circ}\)
- \(225^{\circ}\)
- \(315^{\circ}\)
- \(335^{\circ}\)
Show Worked Solution
\(\text{Coordinates are in the 3rd quadrant.}\)
\(\tan \theta= \dfrac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}} = 1 \)
\(\text{Find reference angle:}\)
\(\theta =\tan^{-1}\left( 1 \right) = 45^{\circ}\)
\(\text{Angle on unit circle}\ = 180+45=225^{\circ}\)
\(\Rightarrow B\)