Trigonometric Functions and Unit Circle

Mrs. Richards introduces trigonometric functions and their operations using the unit circle. She reviews basic trigonometry concepts like SOHCAHTOA and explains how these functions extend beyond right triangles to circular trigonometry. The video covers how to evaluate sine, cosine, and tangent in different quadrants, emphasizing the importance of understanding positive and negative values. The session concludes with practical examples of evaluating trigonometric functions using the unit circle, highlighting the significance of knowing angles and coordinates.

What does the mnemonic SOHCAHTOA help you remember?

• The order of operations

• The definitions of sine, cosine, and tangent

• The properties of quadrilaterals

• The Pythagorean theorem

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CCSS.HSF.TF.A.2

In circular trigonometry, what is the significance of the unit circle?

• It is a tool for solving linear equations

• It is used to define trigonometric functions for all angles

• It is used to measure angles in degrees

• It helps in calculating the area of a circle

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CCSS.HSF.TF.A.2

In which quadrant are both sine and cosine positive?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

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CCSS.HSF.TF.A.2

What is the value of cosine in quadrant II?

• Positive

• Undefined

• Zero

• Negative

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CCSS.HSF.TF.A.2

How is the tangent of an angle related to the unit circle?

• It is the hypotenuse of the triangle

• It is the ratio of y-coordinate to x-coordinate

• It is the y-coordinate of the point

• It is the x-coordinate of the point

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CCSS.HSF.TF.A.2

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

• -1/2

• 1/2

• √3/2

• -√3/2

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CCSS.HSF.TF.A.2

Which trigonometric function is positive in quadrant III?

• Sine

• None

• Cosine

• Tangent

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CCSS.HSF.TF.A.2

What is the cosine of π/3?

• -√3/2

• 1/2

• -1/2

• √3/2

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CCSS.HSF.TF.C.8

How do you simplify the tangent of π/6?

• Multiply by the reciprocal of the denominator

• Add the numerator and denominator

• Subtract the denominator from the numerator

• Divide the numerator by the denominator

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CCSS.HSF.TF.A.2

What is the result of tangent for angles that are multiples of π/4?

• 0

• 1 or -1

• Undefined

• 2 or -2

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CCSS.HSF.TF.A.2