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.

Tags

CCSS.HSF.TF.A.2

Front

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

Back

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

Tags

CCSS.HSF.TF.A.2

Front

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

Back

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

Tags

CCSS.HSF.TF.A.2

Front

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

Back

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

Tags

CCSS.HSF.TF.A.2

Front

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

Back

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

Tags

CCSS.HSF.TF.A.2

Front

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

Back

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

Tags

CCSS.HSF.TF.A.2

Front

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

Back

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

Tags

CCSS.HSF.TF.A.2

Front

What is the relationship between secant and cosine?

Back

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

Tags

CCSS.HSF.TF.A.2

Front

What is the relationship between cosecant and sine?

Back

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

Tags

CCSS.HSF.TF.A.2

Front

In which quadrant is the angle 210 degrees located?

Back

The angle 210 degrees is located in the third quadrant.