Learn to evaluate the half angle for cosine

The video tutorial addresses common misconceptions about cosine, particularly when dealing with angles divided by two. It explains the cosine formula and emphasizes the importance of understanding the difference between Theta and Theta divided by two. The tutorial guides students through solving for Theta, finding coterminal angles, and evaluating cosine values using the unit circle. It concludes with final calculations and simplification of the cosine expression, ensuring students understand the process and can apply it correctly.

What is a common mistake students make when evaluating cosine?

• Ignoring the unit circle

• Not simplifying the fraction

• Forgetting to multiply by pi

• Using the wrong angle in the formula

What is the correct formula for cosine of an angle?

• Square root of 1 plus sine of Theta

• Square root of 1 plus cosine of Theta divided by two

• Square root of 1 minus cosine of Theta

• Square root of 1 plus tangent of Theta

How do you solve for Theta when given Theta divided by two?

• Add pi to both sides

• Subtract pi from both sides

• Multiply both sides by two

• Divide both sides by pi

What is a coterminal angle?

• An angle that is double the original angle

• An angle that is equivalent after adding or subtracting 2π

• An angle that is half of the original angle

• An angle that is a multiple of pi

What is the cosine value for the angle 7π/6 on the unit circle?

• -sqrt(3)/2

• sqrt(3)/2

• -1/2

• 1/2

How can you simplify the expression 1 plus negative sqrt(3)/2 divided by 2?

• Divide the numerator by 2

• Multiply by 2 on the top and bottom

• Subtract 2 from the denominator

• Add 2 to the numerator

What is the final simplified form of the expression 2 minus sqrt(3) over 2?

• 1/2 times (2 - sqrt(3))

• 2 - sqrt(3)

• sqrt(3) - 2

• 1/2 times (sqrt(3) - 2)