Understanding Tangent Equations on the Unit Circle

The video tutorial explains how to solve two tangent equations: tangent theta equals negative one and tangent theta equals square root three divided by three, within the interval from zero to two pi, without using a calculator. The instructor uses reference triangles and the unit circle to determine the solutions. For the first equation, the solutions are found in the second and fourth quadrants, while for the second equation, solutions are in the first and third quadrants. The video emphasizes understanding the geometric representation of these angles and converting between degrees and radians.

What is the primary method used to solve tangent equations in this tutorial?

• Using graphing techniques

• Using algebraic manipulation

• Using reference triangles and the unit circle

• Using a calculator

Tags

CCSS.HSF.TF.A.2

In which quadrants is the tangent function negative?

• Second and fourth

• First and fourth

• Second and third

• First and third

Tags

CCSS.HSF.TF.A.2

What is the reference angle for tangent theta equals negative one?

• 60 degrees

• 45 degrees

• 30 degrees

• 90 degrees

Tags

CCSS.HSF.TF.B.7

What are the radian measures for angles where tangent theta equals negative one?

• Pi over 6 and 5 pi over 6

• Pi over 2 and 3 pi over 2

• 3 pi over 4 and 7 pi over 4

• Pi over 3 and 2 pi over 3

How is the expression square root three divided by three simplified?

• 1 divided by 3

• Square root 3 divided by 3

• Square root 3 divided by 2

• 1 divided by square root 3

Tags

CCSS.HSF.TF.A.2

In which quadrants is the tangent function positive?

• Second and third

• Second and fourth

• First and fourth

• First and third

Tags

CCSS.HSF.TF.A.2

What is the reference angle for tangent theta equals square root three divided by three?

• 90 degrees

• 45 degrees

• 60 degrees

• 30 degrees

Tags

CCSS.HSF.TF.B.7

What are the radian measures for angles where tangent theta equals square root three divided by three?

• Pi over 2 and 3 pi over 2

• Pi over 6 and 7 pi over 6

• 3 pi over 4 and 7 pi over 4

• Pi over 3 and 2 pi over 3

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CCSS.HSG.SRT.C.6

What is the tangent function value for a 30-degree angle in a 30-60-90 triangle?

• 1

• Square root 3

• Square root 3 divided by 2

• 1 divided by square root 3

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CCSS.HSF.TF.A.2

How can the unit circle be used to verify tangent values?

• By checking the sine values

• By checking the cosine values

• By checking the ratio of y to x coordinates

• By checking the radius length

Tags

CCSS.HSF.TF.A.2