# Chapter 5: Trigonometric Functions: Unit Circle Approach

Q1.

Fill in the blanks

If the function $f$is periodic with period $p$, then $f\left(t+p\right)=$______ for every $t$. The trigonometric functions $y=\mathrm{sin}x$and $y=\mathrm{cos}x$ are periodic, with period ______ and amplitude __________. Sketch the graph of each function on the interval $\left[0,2\mathrm{\pi}\right]$.

Q1.

(a) The unit circle is the circle centered at ______ with radius _____.

(b) The equation of the unit circle is ________.

(c) Suppose the point$P\left(x,y\right)$is on the unit circle. Find the missing coordinate:

(i)$P\left(1,\begin{array}{c}\end{array}\right)$

(ii)$P\left(\begin{array}{c}\end{array},1\right)$

(iii) $P\left(-1,\begin{array}{c}\end{array}\right)$

(iv)$P\left(\begin{array}{c}\end{array},-1\right)$

Q1.

Let$P\left(x,y\right)$be the terminal point on the unit circle determined by *$t$*. The $\mathrm{sin}t=$______, $\mathrm{cos}t=$_______, and $\mathrm{tan}t=$______.

Q10.

Find the missing coordinate of *$P$*, using the fact that *$P$* lies on the unit circle in the given quadrant.

Coordinates Quadrant

$P\left(\begin{array}{c}\end{array},-\frac{7}{25}\right)$ IV

Q10.

Find the exact value of the trigonometric function at the given real number.

a.$\mathrm{sin}\frac{3\pi}{4}$

b.$\mathrm{sin}\frac{5\pi}{4}$

c.$\mathrm{sin}\frac{7\pi}{4}$

Q11.

Find the missing coordinate of *$P$*, using the fact that *$P$* lies on the unit circle in the given quadrant.

Coordinates Quadrant

$P\left(\begin{array}{c}\end{array},\frac{1}{3}\right)$ II

Q11.

Find the exact value of the trigonometric function at the given real number.

a.$\mathrm{sin}\frac{7\pi}{3}$

b.$\mathrm{csc}\frac{7\pi}{3}$

c.$\mathrm{cot}\frac{7\pi}{3}$

Q12.

Find the exact value of the trigonometric function at the given real number.

a.$\mathrm{csc}\frac{5\pi}{4}$

b.$\mathrm{sec}\frac{5\pi}{4}$

c.$\mathrm{tan}\frac{5\pi}{4}$

Q12.

Find the missing coordinate of *$P$*, using the fact that *$P$* lies on the unit circle in the given quadrant.

Coordinates Quadrant

$P\left(\frac{2}{5},\begin{array}{c}\end{array}\right)$ I

Q13.

Find the exact value of the trigonometric function at the given real number.

a.$\mathrm{cos}\left(-\frac{\pi}{3}\right)$

b.$\mathrm{sec}\left(-\frac{\pi}{3}\right)$

c.$\mathrm{sin}\left(-\frac{\pi}{3}\right)$