Half Angle Formulas in Trigonometry

The video tutorial introduces half angle formulas in trigonometry, explaining their derivation and application. It covers how to determine the sign of trigonometric functions based on the quadrant of the angle. The tutorial demonstrates evaluating sine, cosine, and tangent using half angle formulas, and solving equations involving these formulas. The importance of using the original angle to determine the sign is emphasized.

What is the formula for the sine of a half angle?

• Plus or minus the square root of (1 + sine u) / 2

• Plus or minus the square root of (1 - cosine u) / 2

• Plus or minus the square root of (1 - sine u) / 2

• Plus or minus the square root of (1 + cosine u) / 2

In which quadrants is the sine function positive?

• Quadrants 3 and 4

• Quadrants 1 and 4

• Quadrants 2 and 3

• Quadrants 1 and 2

Why are half angle formulas useful?

• They are used in calculus for integration

• They simplify trigonometric identities

• They are only useful for angles on the unit circle

• They help find angles not on the unit circle

How can you express 15 degrees using a half angle formula?

• As 60 degrees divided by 4

• As 45 degrees divided by 3

• As 90 degrees divided by 6

• As 30 degrees divided by 2

What is the first step in evaluating the sine of 15 degrees using the half angle formula?

• Use the tangent half angle formula

• Find the cosine of 15 degrees

• Double the angle to 60 degrees

• Rewrite 15 degrees as 30/2

When evaluating cosine of 105 degrees, which quadrant is considered?

• Quadrant 3

• Quadrant 1

• Quadrant 4

• Quadrant 2

What is the cosine of 210 degrees used for in the evaluation of cosine of 105 degrees?

• To determine the sign of the result

• To calculate the tangent of 105 degrees

• To find the sine of 105 degrees

• To simplify the expression

What is the first step in solving equations using half angle formulas?

• Use the double angle formula

• Convert all terms to sine

• Find the derivative of the equation

• Substitute the half angle formula into the equation

How do you handle the sign when squaring a half angle formula?

• The sign remains unchanged

• The sign is inverted

• The sign is doubled

• The sign is eliminated when squaring

What is the solution for cosine squared X equals sine squared X over 2?

• X is pi/4, 3pi/4, and pi

• X is pi/3, 5pi/3, and pi

• X is pi/2, 3pi/2, and pi

• X is pi/6, 5pi/6, and pi