Understanding Trigonometric Expressions

The video tutorial explains how to find the exact value of the expression tangent of two times the inverse sine of negative four-fifths. It begins by modeling the angle on a coordinate plane and sketching a reference triangle. The Pythagorean theorem is used to find the length of the adjacent side. The double angle identity for tangent is then applied to evaluate tangent two theta. The tutorial concludes with the final result of the expression, which is 24/7.

What is the initial expression we are asked to evaluate?

• Cosine of two times inverse tangent

• Tangent of two times inverse sine

• Sine of two times inverse cosine

• Sine of two times inverse tangent

In which quadrant is the angle theta located?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the length of the hypotenuse in the reference triangle?

• 5

• 3

• 4

• 6

Which theorem is used to find the length of the adjacent side?

• Pythagorean theorem

• Sine rule

• Tangent rule

• Cosine rule

What is the value of the adjacent side in the reference triangle?

• 3

• 1

• 2

• 4

What identity is used to evaluate tangent of two theta?

• Double angle identity for sine

• Half angle identity for tangent

• Double angle identity for cosine

• Double angle identity for tangent

What is the value of tangent theta from the reference triangle?

• 4/3

• -4/3

• -3/4

• 3/4

What is the result of simplifying the expression 1 - (16/9)?

• 9/7

• -9/7

• 7/9

• -7/9

What is the final value of the given expression?

• 24/5

• 7/24

• 5/24

• 24/7

What operation is equivalent to dividing by a fraction?

• Multiplying by the reciprocal

• Adding the fraction

• Subtracting the fraction

• Dividing by the reciprocal