Inverse Trigonometric Functions and Secant

The video tutorial explains how to solve a trigonometric equation involving both X and Y. It begins by isolating secant 3X and then uses inverse secant to solve for X. An alternative method using cosine is also demonstrated, showing how secant and cosine are reciprocals. The tutorial provides two acceptable solutions for X, one involving inverse secant and the other involving inverse cosine.

What is the main goal of the trigonometric equation discussed in the video?

• To solve for x in terms of y

• To find the value of y in terms of x

• To calculate the square root of 5

• To determine the value of secant

What is the first step in isolating secant 3x?

• Divide both sides by 3

• Multiply both sides by 2

• Add square root 5 to both sides

• Subtract square root 5 from both sides

After isolating secant 3x, what operation is performed next?

• Subtract y from both sides

• Add y to both sides

• Divide both sides by 2

• Multiply both sides by 3

What function is used to solve for x after isolating secant 3x?

• Inverse secant

• Inverse tangent

• Inverse cosine

• Inverse sine

Which of the following is a correct expression for x using inverse secant?

• x = 1/3 * inverse secant of (y - sqrt(5))/2

• x = 3 * inverse secant of (y - sqrt(5))/2

• x = inverse secant of (y - sqrt(5))/3

• x = inverse secant of 3(y - sqrt(5))/2

What is the relationship between secant and cosine?

• They are equal

• They are reciprocals

• They are inverses

• They are identical

How is the equation rewritten in terms of cosine?

• By using the reciprocal of the secant function value

• By multiplying both sides by 2

• By adding 5 to both sides

• By taking the square root of both sides

What function is used to solve for x when the equation is rewritten in terms of cosine?

• Inverse secant

• Inverse tangent

• Inverse cosine

• Inverse sine

What is the final step to solve for x using inverse cosine?

• Subtract 3

• Add 3

• Divide by 3

• Multiply by 3

Which method can be used to solve the equation involving inverse cosine?

• Add 1/3

• Multiply by 1/3

• Divide by 2

• Multiply by 2