Unit Circle #3B - Third-Quadrant Angles

Front

What is the definition of the unit circle?

Back

The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane, used to define trigonometric functions.

Front

What are the coordinates of the point on the unit circle at an angle of 210 degrees?

Back

The coordinates are \(\left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)\).

Front

What is the value of \(\sec(210^{\circ})\)?

Back

\(\sec(210^{\circ}) = -\frac{2\sqrt{3}}{3}\).

Front

What is the value of \(\sec(225^{\circ})\)?

Back

\(\sec(225^{\circ}) = -\sqrt{2}\).

Front

What is the value of \(\csc(225^{\circ})\)?

Back

\(\csc(225^{\circ}) = -\sqrt{2}\).

Front

What is the value of \(\sec(240^{\circ})\)?

Back

\(\sec(240^{\circ}) = -2\).

Front

What is the value of \(\csc(240^{\circ})\)?

Back

\(\csc(240^{\circ}) = -\frac{2\sqrt{3}}{3}\).

Front

What is the relationship between secant and cosine?

Back

\(\sec(\theta) = \frac{1}{\cos(\theta)}\).

Front

What is the relationship between cosecant and sine?

Back

\(\csc(\theta) = \frac{1}{\sin(\theta)}\).

Front

In which quadrant is the angle 210 degrees located?

Back

The angle 210 degrees is located in the third quadrant.