Unit Circle Trig 4

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. It is used to define trigonometric functions.

Front

What are the coordinates of the point on the unit circle at an angle of \( \frac{\pi}{4} \)?

Back

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

Front

What is the value of \( \sin(\theta) \) for \( \theta = \frac{3\pi}{2} \)?

Back

The value is -1.

Front

What is the value of \( \cos(\theta) \) for \( \theta = \frac{\pi}{3} \)?

Back

The value is \( \frac{1}{2} \).

Front

What is the relationship between sine and cosine on the unit circle?

Back

For any angle \( \theta \), \( \sin(\theta) \) is the y-coordinate and \( \cos(\theta) \) is the x-coordinate of the corresponding point on the unit circle.

Front

What is the value of \( \tan(\theta) \) in terms of sine and cosine?

Back

\( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \).

Front

What is the value of \( \sec(\frac{3\pi}{4}) \)?

Back

The value is \( -\sqrt{2} \).

Front

What is the value of \( \csc(\frac{\pi}{2}) \)?

Back

The value is 1.

Front

What is the value of \( \cot(\frac{\pi}{4}) \)?

Back

The value is 1.

Front

What is the value of \( \sin(\frac{5\pi}{6}) \)?

Back

The value is \( \frac{1}{2} \).