Unit Circle Trig Practice

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.TF.A.2, HSG.SRT.C.6, HSF.TF.A.1

Standards-aligned

Duane Williams

Used 53+ times

FREE Resource

10 Slides • 26 Questions

Evaluating Sine & Cosine with the Unit Circle

Goal: Students will be able to evaluate sine and cosine using the Unit Circle

Using the Unit Circle

to evaluate sine and cosine, we use the coordinates that lie on the Unit Circle's circumference
cosine of an angle is equal to the length of the reference triangle's adjacent side and is represented by the x-coordinate
sine of an angle is equal to the length of the reference triangle's opposite side and is represented by the y-coordinate

Evaluating Cosine

cos(θ) = x-coordinate of the point associated with that angle
cos(270°) = 0
cos(π/6) = √3/2
cos(2π/3) = -1/2

Multiple Choice

Evaluate cos(135°)

$-\frac{\sqrt{2}}{2}$

$\frac{\sqrt{2}}{2}$

$-\frac{\sqrt{3}}{2}$

$-\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

Multiple Choice

Evaluate cos(11π/6)

$-\frac{\sqrt{2}}{2}$

$\frac{\sqrt{2}}{2}$

$-\frac{\sqrt{3}}{2}$

$-\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

Fill in the Blanks

Type answer...

Evaluating Sine

sin(θ) = y-coordinate of the point associated with that angle
sin(4π/3) = -√3/2
sin(0) = 0
sin(135°) = √2/2

Multiple Choice

Evaluate sin(60°)

$\frac{1}{2}$

$\frac{\sqrt{2}}{2}$

$\frac{\sqrt{3}}{2}$

Multiple Choice

sin(7π/6)

- ½

√3 /2

-√3 /2

-√2 /2

Multiple Choice

sin 180°

-1

$-\frac{\sqrt{3}}{2}$

$\frac{1}{2}$

The Other Trigonometric Functions

Values of cotangent, secant and cosecant

Multiple Choice

REVIEW

What is sin 30°?

^√3/₂

^√2/₂

Multiple Choice

REVIEW

What is cos 90°?

undefined

Multiple Choice

REVIEW

What is sin 45°?

^√3/₂

^√2/₂

Multiple Choice

REVIEW

What is cos 60°?

^√3/₂

^√2/₂

The TANGENT (TOA) Function - A reminder

The TANGENT of an angle is defined in Geometry by the ratio of the opposite side and adjacent side.
The TANGENT of an angle is defined by the UNIT CIRCLE as y/x.
The TANGENT of an angle in Trigonometry is defined by the ratio of sinΘ and cosΘ

Multiple Choice

The GEOMETRY use of TANGENT;

Find the trig value. Take note you are looking for the tangent of angle C.

Multiple Choice

One - more:

Find the trig value. Again, stating the tangent of C.

The Trigonometry Use

The tangent is equivalent to the sin value divided by the cosine value. Which is the same idea as y divided by cosine? Right??

Multiple Choice

Which of the following is the value of;

(It might be helpful to convert to a degree first.)

$\tan\left(\frac{7\pi}{4}\right)$

-1

√2/2

undefined

Multiple Choice

Which of the following is the value of;

(It might be helpful to convert to a degree first.)

$\tan\left(-\pi\right)$

undefined

-1

Multiple Choice

Which of the following is the value of;

(It might be helpful to convert to a degree first.)

$\tan\left(\frac{7\pi}{6}\right)?$

√3/3

√3

$-\frac{\sqrt{3}}{3}$

$-\sqrt{3}$

The Reciprocal Functions

The three main trigonometric function values are ratios and ratios have reciprocals.
The reciprocal of sine is COSECANT (CSC).
The reciprocal of cosine is SECANT (SEC)
The reciprocal of tangent is COTANGENT (COT)

So if they are reciprocals of one another

If sinA = 3/5 then cscA = 5/3
If cosA = 4/5 then secA =5/4
If tanA = 3/4 then cotA = 4/3

Multiple Choice

Let's practice some reciprocals...

Given $\frac{5}{9}$ , the reciprocal would be ___.

$\frac{9}{5}$

$\frac{5}{9}$

Neither of these

Multiple Choice

Let's practice some reciprocals...

Given $\frac{15}{7}$ , the reciprocal would be ___.

$\frac{7}{15}$

$\frac{15}{7}$

Neither of these

Multiple Choice

How about this?

Given $\frac{\pi}{180}$ , the reciprocal would be ___.

$\frac{180}{\pi}$

$\frac{\pi}{180}$

Neither of these

Consider this then;

Multiple Choice

What is the reciprocal of the sine (sin) function?

cosecant (csc)

cosine (cos)

secant (sec)

cotangent (cot)

Multiple Choice

Cotangent (cot) is the reciprocal of what function?

Cosecant (csc)

Sine (sin)

Cosine (cos)

Tangent (tan)

Multiple Choice

What is the reciprocal of the cosine (cos) function?

cosecant (csc)

cosine (cos)

secant (sec)

cotangent (cot)

Multiple Choice

Which of the following is the exact value of;

csc(30^o).

(Remember csc is the reciprocal of sin.)

$\frac{\sqrt{3}}{3}$

$\frac{2\sqrt{3}}{3}$

$\sqrt{2}$

undefined

Multiple Choice

Which of the following is the exact value of;

cot(135^o)

(Remember...cot is the reciprocal of tan)

-1

$\sqrt{2}$

undefined

Multiple Choice

Which of the following is the exact value of; $\csc\left(\frac{\pi}{2}\right)$

(Remember, csc is the reciprocal of sin)

-1

$\frac{\sqrt{3}}{3}$

$\sqrt{2}$

undefined

Multiple Choice

Which of the following is the exact value of;

$\cot\left(\pi\right)$

(Remember, cot is the reciprocal of tan)

-2

$\frac{\sqrt{3}}{3}$

$\frac{2\sqrt{3}}{3}$

$\sqrt{2}$

undefined

Multiple Choice

Not all angles are exact value angles. Consider this.

Given $\cos\theta=-\frac{2}{3}$ the $\sec\theta$ =?

$-\frac{2}{3}$

$-\frac{3}{2}$

$\frac{3}{2}$

$\frac{2}{3}$

Evaluating Sine & Cosine with the Unit Circle

Goal: Students will be able to evaluate sine and cosine using the Unit Circle

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