Understanding Inverse Trigonometric Equations

The video tutorial explains how to solve an equation involving inverse trigonometric functions, specifically inverse cosine and inverse sine. It begins by isolating the variable x and taking the cosine of both sides. The tutorial then focuses on understanding the angle theta derived from inverse sine, its range, and how it fits within the trigonometric circle. A reference triangle is used to model the angle, and the Pythagorean theorem is applied to find the missing side. Finally, the solution is derived, showing that x equals 12/13, and the key steps are summarized.

What is the first step in solving the equation involving inverse cosine and inverse sine?

• Isolate the variable X

• Multiply both sides by 2

• Subtract 13 from both sides

• Add 5 to both sides

What is the range of the inverse sine function?

• 0 to PI

• -PI to PI

• -PI/2 to PI/2

• 0 to 2PI

In which quadrant does the angle theta terminate if sine theta is negative?

• Fourth quadrant

• First quadrant

• Second quadrant

• Third quadrant

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

• 5

• 10

• 12

• 13

Which theorem is used to find the missing side of the reference triangle?

• Pythagorean theorem

• Sine rule

• Cosine rule

• Tangent rule

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

• 5

• 12

• 10

• 13

What is the cosine of angle theta in the reference triangle?

• 13/12

• 5/13

• 5/12

• 12/13

What is the final solution for X in the given equation?

• 13/12

• 5/13

• 12/13

• 13/5

What does the inverse sine of -5/13 represent?

• An angle with a cotangent value of -5/13

• An angle with a cosine value of -5/13

• An angle with a sine value of -5/13

• An angle with a tangent value of -5/13

What is the key to solving equations involving inverse trigonometric functions?

• Identifying the specific interval

• Applying the tangent rule

• Recognizing the angle's quadrant

• Using the sine rule