Master Evaluating the half angle for sine, cosine, and tangent given an angle

The video tutorial explains how to evaluate trigonometric expressions using the half angle formulas for sine, cosine, and tangent. It begins with an introduction to the half angle formula for sine, followed by a detailed application to find the sine of 15 degrees. The tutorial then covers the cosine half angle formula, demonstrating its use with an example. Finally, the tangent half angle formula is introduced and applied to solve a trigonometric expression. Throughout the video, the instructor emphasizes understanding the formulas and their applications in different quadrants.

Why is the half angle formula used for angles like 15 degrees?

• Because 15 degrees is a right angle.

• Because 15 degrees is an obtuse angle.

• Because 15 degrees is not a point where the angle crosses the unit circle.

• Because 15 degrees is a common angle on the unit circle.

What is the half angle formula for sine?

• Sine of Theta divided by 2 equals plus or minus sqrt 1 plus cosine of Theta divided by two.

• Sine of Theta divided by 2 equals plus or minus sqrt 1 minus cosine of Theta divided by two.

• Sine of Theta divided by 2 equals plus or minus sqrt 1 plus sine of Theta divided by two.

• Sine of Theta divided by 2 equals plus or minus sqrt 1 minus sine of Theta divided by two.

In which quadrant is the angle 15 degrees located?

• Second quadrant

• Third quadrant

• Fourth quadrant

• First quadrant

What is the cosine of 30 degrees on the unit circle?

• 0

• sqrt 2 / 2

• 1/2

• sqrt 3 / 2

What is the half angle formula for cosine?

• Cosine of Theta divided by 2 equals plus or minus sqrt 1 minus cosine of Theta divided by two.

• Cosine of Theta divided by 2 equals plus or minus sqrt 1 plus sine of Theta divided by two.

• Cosine of Theta divided by 2 equals plus or minus sqrt 1 plus cosine of Theta divided by two.

• Cosine of Theta divided by 2 equals plus or minus sqrt 1 minus sine of Theta divided by two.

What is the cosine of 315 degrees?

• 0

• 1/2

• sqrt 3 / 2

• sqrt 2 / 2

What is the half angle formula for tangent?

• Tangent of Theta divided by 2 equals plus or minus sqrt 1 minus sine of Theta divided by 1 plus sine of Theta.

• Tangent of Theta divided by 2 equals plus or minus sqrt 1 minus cosine of Theta divided by 1 plus cosine of Theta.

• Tangent of Theta divided by 2 equals plus or minus sqrt 1 plus sine of Theta divided by 1 minus sine of Theta.

• Tangent of Theta divided by 2 equals plus or minus sqrt 1 plus cosine of Theta divided by 1 minus cosine of Theta.

In which quadrant is the angle 3π/4 located?

• Third quadrant

• First quadrant

• Fourth quadrant

• Second quadrant

What is the cosine of 3π/4?

• -1/2

• -sqrt 3 / 2

• -sqrt 2 / 2

• 0

What is the final simplified form of the tangent half angle formula for 3π/8?

• Sqrt 3 - 2 sqrt 2

• Sqrt 2 - 2 sqrt 3

• Sqrt 3 + 2 sqrt 2

• Sqrt 2 + 2 sqrt 3