Example: For each of the expressions below, use the unit circle to determine the exact value.
- \(\cos\left(-\dfrac{2\pi}{{3}}\right)\)
- \(\sin\left(\dfrac{5\pi}{{4}}\right)\)
- \(\tan\left(-\dfrac{7\pi}{{6}}\right)\)
Solution Sketch out the unit circle and determine the appropriate point on the circle by using the reflections method to copy the first quadrant values to their respective points. Then, the Cosine is the \(x\) coordinate, Sine is the \(y\) coordinate, and Tangent is \(\dfrac{{y}}{{x}}\).
- \(\cos\left(-\dfrac{2\pi}{{3}}\right)=-\dfrac{{1}}{{2}}\)
- \(\sin\left(\dfrac{5\pi}{{4}}\right)=-\dfrac{\sqrt{{2}} }{{2}}\)
- \(\tan\left(-\dfrac{7\pi}{{6}}\right)=\dfrac{-1/2}{\sqrt{{3}}/2}=-\dfrac{{1}}{\sqrt{ 3 } }=-\dfrac{\sqrt{{3}}}{{3}}\)