Trigonometric Functions and Their Applications

The video tutorial explains how to evaluate the tangent of a half angle, specifically when the angle is represented as pi over 12. It discusses the use of tangent formulas, including sine over one plus cosine and one minus cosine over sine. The instructor emphasizes that either formula can be used, but prefers using monomials in the denominator. The video also addresses common misconceptions about plugging in values for theta and demonstrates how to solve for theta by multiplying both sides by two. Finally, it evaluates the trigonometric functions for pi over 6 using the unit circle.

What is the initial angle given in the video?

• pi over 6

• pi over 12

• pi over 3

• pi over 4

What is the half-angle formula used for tangent?

• One minus sine over cosine

• Cosine over sine

• Sine over one plus cosine

• Sine over cosine

Which formula does the teacher prefer to use for tangent?

• Sine over cosine

• Sine over one plus cosine

• One minus cosine over sine

• Cosine over sine

What is a common misconception students have about theta?

• Theta is pi over 12

• Theta is pi over 6

• Theta is pi over 4

• Theta is pi over 3

How do you determine the value of theta?

• Divide by 2

• Subtract 2

• Multiply by 2

• Add 2

What is the value of theta after calculation?

• pi over 6

• pi over 3

• pi over 12

• pi over 4

Can pi over 12 be evaluated using the unit circle?

• Only for sine

• Only for cosine

• Yes

• No

What is the cosine of pi over 6?

• 3/2

• Square root of 2 over 2

• Square root of 3 over 2

• 1/2

What is the sine of pi over 6?

• 1/2

• 3/2

• Square root of 3 over 2

• Square root of 2 over 2

What operation is used to simplify the expression with twos in the denominator?

• Division

• Multiplication

• Subtraction

• Addition