Understanding Trigonometric Expressions

The video tutorial explains how to find the exact value of the expression cosine of two times the inverse sine of negative 12/13. It begins by discussing the inverse sine function and its output as an angle theta. The tutorial then introduces the double angle identity for cosine, which involves sine theta, and shows how to use it to simplify the expression. By substituting known values and performing calculations, the exact value is determined. The video concludes with a brief mention of an alternative method to find the value.

What is the main objective of the problem discussed in the video?

• To solve a quadratic equation

• To calculate the tangent of an angle

• To determine the exact value of a cosine expression

• To find the sine of an angle

What does the inverse sine of negative 12/13 represent?

• An angle theta

• A tangent value

• A cosine value

• A logarithmic value

In which interval does the angle theta lie when considering the inverse sine function?

• 0 to 180 degrees

• -180 to 180 degrees

• 0 to 360 degrees

• -90 to 90 degrees

Which identity is used to express cosine of two theta in terms of sine?

• cosine two theta equals one plus sine squared theta

• cosine two theta equals sine squared theta

• cosine two theta equals one minus two sine squared theta

• cosine two theta equals two sine theta

What is the value of sine theta in the given problem?

• 13/12

• -13/12

• -12/13

• 12/13

What is the first step in using the double angle identity for cosine?

• Calculating the square of cosine theta

• Finding the tangent of theta

• Determining the angle theta

• Substituting the value of sine theta

What is the result of squaring negative 12/13?

• 13/144

• 144/169

• 12/169

• 169/144

What is the final result of the expression cosine of two theta?

• -288/169

• 288/169

• -119/169

• 119/169

What is the purpose of using the double angle identity in this problem?

• To simplify the expression

• To find the value of theta

• To convert sine to cosine

• To calculate the tangent

What is the significance of the final result in the context of the problem?

• It calculates the tangent of theta

• It determines the angle theta

• It provides the exact value of the original expression

• It verifies the value of sine theta