Understanding Angles and Trigonometric Functions

This video tutorial explains how to determine angles and trigonometric function values without using common reference angles. The problem involves finding the angle theta and the five other trigonometric function values given that cosine theta is -6/19 and theta is in the third quadrant. The tutorial covers constructing a reference triangle, using the Pythagorean theorem, and calculating all six trigonometric function values. It also demonstrates how to use a calculator to find the angle theta and rationalize trigonometric ratios.

What is the main goal of the lesson discussed in the video?

• To solve algebraic equations using trigonometry.

• To find angles and trigonometric values given one trig function value.

• To determine angles using common reference angles.

• To understand the history of trigonometry.

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CCSS.HSF.TF.A.2

In which quadrant is angle theta located according to the problem?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What theorem is used to find the missing side of the reference triangle?

• Sine Rule

• Pythagorean Theorem

• Tangent Rule

• Cosine Rule

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CCSS.8.G.B.8

What is the value of the missing side calculated using the Pythagorean theorem?

• 7 square roots of 13

• 6 square roots of 13

• 5 square roots of 13

• 8 square roots of 13

What is the approximate angle theta in degrees as determined using the calculator?

• 108.4 degrees

• 251.6 degrees

• 71.6 degrees

• 180 degrees

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CCSS.HSG.SRT.C.7

Which trigonometric function is the reciprocal of cosine?

• Sine

• Tangent

• Cosecant

• Secant

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CCSS.HSF.TF.C.8

What is the value of sine theta calculated from the reference triangle?

• -5 square roots of 13 divided by 19

• -6 square roots of 13 divided by 19

• -8 square roots of 13 divided by 19

• -7 square roots of 13 divided by 19

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CCSS.HSG.SRT.C.6

What is the value of tangent theta based on the reference triangle?

• 5/6

• 6/5

• 7/5

• 5/7

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CCSS.HSF.TF.A.2

What is the reciprocal of the tangent function?

• Sine

• Cosine

• Cotangent

• Secant

What is the purpose of rationalizing trigonometric ratios?

• To convert to radians

• To change the angle

• To make the expression more complex

• To simplify the expression