Unit Circle Practice

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.

Front

What are the coordinates of the point on the unit circle corresponding to an angle of \( \theta \)?

Back

The coordinates are \( (\cos \theta, \sin \theta) \).

Front

What is the relationship between secant and cosine?

Back

Secant is the reciprocal of cosine: \( \sec \theta = \frac{1}{\cos \theta} \).

Front

What is the value of \( \sec \theta \) for the point \( \left(\frac{\sqrt{5}}{5}, \frac{2\sqrt{5}}{5}\right) \)?

Back

The value of \( \sec \theta \) is \( \frac{\sqrt{5}}{ } \).

Front

What is the value of \( \sin \theta \) for the point \( \left(\frac{\sqrt{5}}{5}, \frac{2\sqrt{5}}{5}\right) \)?

Back

The value of \( \sin \theta \) is \( \frac{2\sqrt{5}}{5} \).

Front

What is the value of \( \tan(-\pi) \)?

Back

The value of \( \tan(-\pi) \) is 0.

Front

What is the definition of cosecant?

Back

Cosecant is the reciprocal of sine: \( \csc \theta = \frac{1}{\sin \theta} \).

Front

How do you solve \( \csc x = -2 \) in the interval \( [0, 2\pi) \)?

Back

The solutions are \( \frac{7\pi}{6}, \frac{11\pi}{6} \).

Front

What is the value of \( \csc(3\pi/4) \)?

Back

The value of \( \csc(3\pi/4) \) is \( \sqrt{2} \).

Front

What is the relationship between sine and cosecant?

Back

Cosecant is the reciprocal of sine: \( \csc \theta = \frac{1}{\sin \theta} \).