Understanding Sine 112.5 Degrees Using Half-Angle Identity

The video tutorial explains how to determine the exact value of sine 112.5 degrees using a half-angle identity. It begins by introducing the concept of half-angle identities and calculating the value of 'a'. The tutorial then applies the half-angle identity, using reference triangles to find cosine 225 degrees, and simplifies the expression to find the exact sine value. Finally, the result is verified using a calculator.

What is the purpose of using a half-angle identity in this context?

• To calculate the tangent of 112.5 degrees

• To determine the quadrant of 112.5 degrees

• To approximate the value of cosine 112.5 degrees

• To find the exact value of sine 112.5 degrees

If a divided by two equals 112.5 degrees, what is the value of 'a'?

• 225 degrees

• 337.5 degrees

• 112.5 degrees

• 450 degrees

In which quadrant is 112.5 degrees located, and what is the sign of the sine function there?

• First quadrant, positive

• Second quadrant, positive

• Third quadrant, negative

• Fourth quadrant, negative

What is the significance of the positive square root in the sine function value?

• It suggests the angle is in the fourth quadrant

• It confirms the angle is in the third quadrant

• It shows the angle is in the second quadrant

• It indicates the angle is in the first quadrant

What is the cosine of 225 degrees using a reference triangle?

• -√2/2

• √2/2

• -1/√2

• 1/√2

How do you simplify the expression for sine 112.5 degrees?

• By multiplying the fraction under the square root by 2/2

• By multiplying the numerator by 4

• By adding 1 to the numerator

• By rationalizing the denominator

What is the exact value of sine 112.5 degrees after simplification?

• √(2 + √2) / 2

• √(2 - √2) / 2

• √(2 + 2√2) / 4

• √(2 - 2√2) / 4

Why is it important to verify the exact value using a calculator?

• To check the tangent value

• To confirm the accuracy of the exact value

• To find the cosine of 112.5 degrees

• To ensure the calculator is in degree mode

What should you check on the calculator before finding the sine of 112.5 degrees?

• That it is in radian mode

• That it is in graphing mode

• That it is in degree mode

• That it is in scientific mode

What is the decimal approximation process for sine 112.5 degrees?

• Subtract 1 from the exact value

• Convert the exact value to a decimal

• Multiply the exact value by 2

• Divide the exact value by 4