Unit Circle and Trigonometric Functions

The video explores the unit circle and its extension of the traditional SOH-CAH-TOA definitions of trigonometric functions. It reviews the limitations of SOH-CAH-TOA for angles approaching or exceeding 90 degrees and introduces the unit circle as a solution. The unit circle is explained with a focus on its definition of sine and cosine, using 30-60-90 triangles to demonstrate consistency with SOH-CAH-TOA. The video concludes by highlighting the unit circle's ability to handle angles beyond 90 degrees and even negative angles, offering a comprehensive understanding of trigonometric functions.

What is the primary purpose of studying the unit circle in trigonometry?

• To solve algebraic equations

• To extend the traditional SOH-CAH-TOA definitions

• To understand the properties of circles

• To measure angles in degrees

Tags

CCSS.HSG.SRT.C.6

According to SOH-CAH-TOA, what is the sine of an angle in a right triangle?

• Adjacent side over hypotenuse

• Opposite side over hypotenuse

• Adjacent side over opposite side

• Opposite side over adjacent side

Tags

CCSS.HSG.SRT.C.6

Why does the traditional SOH-CAH-TOA definition become problematic for angles approaching 90 degrees?

• It only works for angles less than 45 degrees

• It cannot have two 90 degree angles in a right triangle

• It cannot handle negative angles

• It requires a non-right triangle

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CCSS.HSF.TF.A.2

What is the radius of a unit circle?

• 0

• 1

• π

• 2

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CCSS.HSF.TF.A.2

In the unit circle definition, what does the cosine of an angle represent?

• The angle in degrees

• The x-coordinate where the radius intersects the unit circle

• The length of the hypotenuse

• The y-coordinate where the radius intersects the unit circle

Tags

CCSS.HSF.TF.A.2

For a 30-degree angle in a unit circle, what is the sine value?

• 0

• 1

• 1/2

• √3/2

Tags

CCSS.HSG.CO.C.10

In a 30-60-90 triangle, what is the length of the side opposite the 30-degree angle if the hypotenuse is 1?

• √2/2

• 1/2

• √3/2

• 1

Tags

CCSS.HSG.SRT.C.7

How does the unit circle definition extend the SOH-CAH-TOA definition?

• By ignoring the hypotenuse

• By allowing calculations for angles greater than 90 degrees

• By simplifying the calculations

• By using only right triangles

Tags

CCSS.HSG.SRT.C.6

What is the relationship between the tangent function and the unit circle?

• Tangent is the x-coordinate over the y-coordinate

• Tangent is the y-coordinate over the x-coordinate

• Tangent is the hypotenuse over the adjacent side

• Tangent is the opposite side over the hypotenuse

Tags

CCSS.HSF.TF.A.2

What is the sine of 330 degrees in the unit circle?

• -√3/2

• -1/2

• 1/2

• √3/2

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CCSS.HSF.TF.A.2