Half Angle Identities and Quadrants

This video tutorial covers the use of half angle identities to determine function values in trigonometry. It begins with an introduction to half angle identities and their derivation, followed by practical examples. The video demonstrates how to calculate the sine of Pi/8 and the cosine of 105 degrees using these identities. It also explains how to find the cosine, sine, and tangent of A/2 when given specific conditions. The tutorial emphasizes careful algebraic manipulation and understanding of trigonometric principles.

What is the primary purpose of using half angle identities?

• To simplify complex numbers

• To determine function values

• To solve quadratic equations

• To find derivatives

What must be considered when using half angle identities with a plus or minus sign?

• The length of the hypotenuse

• The quadrant of angle A/2

• The angle's degree

• The type of triangle

What is the first step in finding the exact value of sine pi/8?

• Find the value of angle A

• Sketch the unit circle

• Use a calculator

• Memorize the identity

Which reference angle is used to find sine pi/8?

• Pi/4

• Pi/6

• Pi/3

• Pi/2

What is the cosine of 210 degrees used for in the video?

• To find tangent of 45 degrees

• To find cosine of 105 degrees

• To find sine of 30 degrees

• To find sine of pi/8

In which quadrant does 105 degrees fall?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the cosine value of angle A given in the second quadrant?

• -1/3

• -3/4

• -2/3

• -1/2

What is the significance of angle A/2 being in the first quadrant?

• Only sine is positive

• Only cosine is positive

• All function values are positive

• All function values are negative

What is the third side of the reference triangle when cosine A is -2/3?

• Square root of 4

• Square root of 3

• Square root of 6

• Square root of 5

What is the tangent of A/2 when cosine A is -2/3?

• Square root of 4

• Square root of 3

• Square root of 5

• Square root of 6