Exploring Trigonometric Functions: Sine, Cosine, and More

Professor Dave introduces trigonometric functions, starting with a recap of radians and circles. He explains the role of triangles in trigonometry using the coordinate plane, defining sine, cosine, and tangent with the mnemonic SOHCAHTOA. The video covers reciprocal functions like cosecant, secant, and cotangent. It concludes with evaluating trigonometric functions for special triangles, emphasizing the importance of memorizing key values.

What is the primary focus of trigonometry?

• Polygons

• Circles

• Squares

• Triangles

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CCSS.HSG.SRT.D.11

In a right triangle, what is the hypotenuse?

• The longest side

• The side adjacent to the right angle

• The shortest side

• The side opposite the right angle

What does the mnemonic SOHCAHTOA help you remember?

• The relationships between the sides of a triangle

• The angles in a triangle

• The names of the trigonometric functions

• The formulas for sine, cosine, and tangent

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What is the sine of an angle in a right triangle?

• Hypotenuse over opposite

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Opposite over adjacent

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CCSS.HSG.SRT.C.6

What is the reciprocal of the sine function?

• Secant

• Tangent

• Cotangent

• Cosecant

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If the cosine of an angle is 4/5, what is the secant of the same angle?

• 5/3

• 1/4

• 4/5

• 5/4

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CCSS.HSG.SRT.C.7

For a triangle with sides 5, 12, and 13, what is the sine of the angle opposite the side of length 5?

• 5/13

• 5/12

• 12/13

• 13/5

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CCSS.HSG.SRT.C.6

In a 30-60-90 triangle, what is the length of the hypotenuse if the shorter leg is 1?

• 1

• √3

• 2

• √2

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What is the tangent of a 45-degree angle?

• 1

• √2

• √3

• 1/√2

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CCSS.HSG.SRT.C.6

What is the cosine of a 60-degree angle?

• 1/2

• √3/2

• 1/√2

• √3

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