Understanding Sine Pi Over 12 Using Identities

The video tutorial explains how to determine the exact value of sine pi over 12 radians using a half-angle identity, also known as a power-reducing formula. It demonstrates the process of applying the identity, using a reference triangle to find cosine pi over 6, and simplifying the expression to find the exact sine value. The tutorial concludes by comparing the result with previous findings, emphasizing the consistency of the method.

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

• To find the approximate value of sine pi over 12

• To determine the exact value of sine pi over 12

• To convert radians to degrees

• To simplify trigonometric expressions

What is pi over 12 radians equivalent to in degrees?

• 30 degrees

• 45 degrees

• 15 degrees

• 60 degrees

Which identity is used to express sine squared a in terms of cosine?

• Sine double angle identity

• Cosine double angle identity

• Power-reducing formula

• Sum and difference formula

What is the value of cosine pi over six?

• Square root 3 divided by 2

• 1/2

• Square root 2 divided by 2

• 3/2

In which quadrant is pi over 12 radians located?

• Third quadrant

• Second quadrant

• Fourth quadrant

• First quadrant

What is the simplified form of sine squared pi over 12?

• Two minus square root three all over four

• One plus square root three all over four

• Square root three minus two all over four

• Two plus square root three all over four

Why is the sine value positive for pi over 12 radians?

• Because it is in the fourth quadrant

• Because it is in the third quadrant

• Because it is in the first quadrant

• Because it is in the second quadrant

What is the final exact value of sine pi over 12?

• Square root of 2 minus square root 3 all over 2

• Square root of 2 plus square root 3 all over 2

• Square root of 3 plus square root 2 all over 2

• Square root of 3 minus square root 2 all over 2

What is the significance of the square root in the final step?

• It determines the sign of the sine value

• It finds the cosine value

• It simplifies the expression

• It converts radians to degrees

How does the sine value found using the half-angle identity compare to the one found using the power-reducing formula?

• They are different

• They are the same

• One is more complex

• One is an approximation