Task Sets: Extend trigonometric functions using unit circle - Common Core Math - HS Functions

1.

The terminal side of angle $\theta$ intersects the unit circle at the
point $(-0.6,\ 0.8)$ . Using the unit circle definition of
trigonometric functions, what is $\sin(\theta)$ ?
Enter a decimal value.

2.

An angle $\theta$ has its terminal side in Quadrant III. Which
statement correctly describes the signs of $\sin(\theta)$ and
$\cos(\theta)$ ?

A.

$\sin(\theta) > 0$ and $\cos(\theta) > 0$

B.

$\sin(\theta) > 0$ and $\cos(\theta) < 0$

C.

$\sin(\theta) < 0$ and $\cos(\theta) < 0$

D.

$\sin(\theta) < 0$ and $\cos(\theta) > 0$

3.

A student says, "Sine and cosine are only defined for angles between
$0$ and $2\pi$ ." Which response best corrects this statement?

A.

The student is correct; angles outside $[0, 2\pi)$ are
not standard positions and cannot be evaluated.

B.

The unit circle wraps around continuously, so $\sin$ and $\cos$
are defined for any real number input by identifying the
corresponding point on the circle.

C.

Sine and cosine are defined for angles up to $4\pi$ , since the
unit circle completes two full rotations.

D.

Only negative angles are excluded; all non-negative angles are
valid inputs for sine and cosine.

HSF.TF.A.2 Tutor Intake — Unit Circle and Extended Trig Functions

Concepts

Procedures