#### (a)

$$
28^circ
$$

#### (b)

$3360^circ-28^circ=332^circ$

(a) $28^circ$; (b) $332^circ$

#### (a)

Side opposite: $-4$

Side adjacent: $3$

Hypotenuse: $h^2=3^2+4^2$

$h^2=25$

$h=5$

$sin theta=-dfrac{4}{5}$, $cos theta=dfrac{3}{5}$, $tan theta=-dfrac{4}{3}$,

$csctheta=-dfrac{5}{4}$, $sectheta=dfrac{5}{3}$, $cottheta=-dfrac{3}{4}$

#### (b)

$theta=sin^{-1}left(-dfrac{4}{5} right)$

$theta=307^{circ}$

The principal angle is $360^{circ}-53^{circ}=307^{circ}$

(a) see solution; (b) $307^circ$.

#### (a)

$sin60^{circ}=dfrac{sqrt{3}}{2}$

#### (b)

$tan 180^{circ}=dfrac{0}{1}=0$

#### (c)

$sin 120^{circ}=dfrac{sqrt{3}}{2}$

#### (d)

$cos 300^{circ}=dfrac{1}{2}$

#### (e)

$sec 135^{circ}=-dfrac{sqrt{2}}{1}=-sqrt{2}$

#### (f)

$csc 270^{circ}=dfrac{1}{-1}=-1$

#### (a)

Since cosine is positive in the first and fourth quadrants, $theta=60^{circ}$,$300^{circ}$

#### (b)

Sincetangent is positive in the first and third quadrants, $theta=30^{circ}$,$210^{circ}$

#### (c)

Since tangent is positive in the first and third quadrants, $theta=45^{circ}$,$225^{circ}$

#### (d)

Cosine equals $-1$ at $theta=180^{circ}$

#### (e)

Contangent equals $-1$ at $theta=135^{circ}, 315^{circ}$

#### (f)

Sine equals $1$ at $theta=90^{circ}$

#### (a)

$$
textbf{Period=$360^circ$, amplitude=$1$, $y=0, R=left{yinBbb{R}|-1 leq y leq 1 right}$}
$$

#### (b)

$$
textbf{Period=$360^circ$, amplitude=$1$, $y=0, R=left{yinBbb{R}| -1 leq y leq 1 right}$}
$$

#### (a)

$textbf{period}$ = $dfrac{2cdot180}{3}=120$, $y=0$, $45^circ$ to the left, $textbf{amplitude}$=$2$.

#### (a)

$textbf{period}$ = $dfrac{2cdot180}{dfrac{1}{2}}=720$, $y=-1$, $60^circ$ to the right, $textbf{amplitude}$=$1$.

$a$ is the amplitude, which determines how far above and below the axis of the curve of the function rises and falls; $k$ defines the period of the function, which is now often the function repeats itself; $d$ is the horizontal shift, which shifts the function to the right or the left; and $c$ is the vertical shift of the function.