Use Unit Circle to find sine, cosine, tangent

Presentation

•

Mathematics

•

9th - 12th Grade

•

Medium

•

CCSS

HSF.TF.A.2

Standards-aligned

Yao Xu

Used 4+ times

FREE Resource

2 Slides • 8 Questions

Using the Unit Circle

To use the Unit Circle to evaluate cosine, sine, or tangent we use the coordinates of the point of intersection between the terminal side of the angle and the Unit Circle.
The x-coordinate of the point is equal to the cosine of the angle.
The y-coordinate of the point is equal to the sine of the angle.
To find the tangent of an angle you take the y-coordinate/x-coordinate.

Multiple Choice

What is the exact coordinates of 3π/4 on the unit circle?

(−√2∕2, √2∕2)

(−√2∕2, −√2∕2)

(−√3∕2, −√2∕2)

(√2∕2, −√2∕2)

Multiple Choice

Given the ordered pair (-¹/₂ , ^√3/₂), what is the value of cosine?

√3

^-1/₂

^√3/₂

^√3/₃

Multiple Choice

What is cos 60°?

^√3/₂

^√2/₂

Multiple Choice

sin π/4

√2∕2

1/2

√3/2

Evaluate Tangent

Tan(angle) = y-coordinate/x-coordinate
Tangent is positive in the FIRST and THIRD quadrants.
Tangent is negative in the SECOND and FOURTH quadrants.
tan(90°) = 1/0 = UNDEFINED
tan(π) = 0/-1 = 0
tan(240°) = (-√3/2)/(-1/2)
=(-√3/2) *(-2/1) = √3/1 = √3

Multiple Choice

What is tan 45°?

^√2/₂

^√3/₂

Multiple Choice

Evaluate $\tan\left(\frac{\pi}{2}\right)$

$\frac{1}{0}$ undefined

$\frac{0}{1}$

Multiple Choice

Find the exact value of $\tan\left(\frac{7\pi}{6}\right)$

$-\frac{1}{2}$

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

$\frac{1}{\sqrt{\ 3}}$

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

Multiple Choice

Using the reference angle, find the exact value of $\tan\left(\frac{5\pi}{3}\right)$ .

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

$-1$

$-\sqrt[]{3}$

$\sqrt[]{3}$

Using the Unit Circle

To use the Unit Circle to evaluate cosine, sine, or tangent we use the coordinates of the point of intersection between the terminal side of the angle and the Unit Circle.
The x-coordinate of the point is equal to the cosine of the angle.
The y-coordinate of the point is equal to the sine of the angle.
To find the tangent of an angle you take the y-coordinate/x-coordinate.

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