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.

Tags

CCSS.HSF.TF.A.2

Front

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

Back

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

Tags

CCSS.HSF.TF.A.2

Front

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

Back

The value is -1.

Tags

CCSS.HSF.TF.A.2

Front

What is the value of \( \cos(\theta) \) for \( \theta = \pi \)?

Back

The value is -1.

Tags

CCSS.HSF.TF.A.2

Front

What is the relationship between \( \sin \) and \( \cos \) on the unit circle?

Back

For any angle \( \theta \), the coordinates on the unit circle are given by \( (\cos(\theta), \sin(\theta)) \).

Tags

CCSS.HSF.TF.A.2

Front

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

Back

The value is 1.

Tags

CCSS.HSF.TF.A.2

Front

What is the secant function in terms of cosine?

Back

The secant function is defined as \( \sec(\theta) = \frac{1}{\cos(\theta)} \).

Tags

CCSS.HSF.TF.A.2

Front

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

Back

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

Tags

CCSS.HSF.TF.A.2

Front

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

Back

The value is 2.

Tags

CCSS.HSF.TF.A.2

Front

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

Back

The value is \( \frac{1}{\sqrt{3}} \) or \( \frac{\sqrt{3}}{3} \).

Tags

CCSS.HSF.TF.A.2