Trigonometric Functions and Equations

This video tutorial covers solving trigonometric equations involving inverse trigonometric functions. It includes three examples: solving an equation with sine, an equation with arctangent, and an equation involving both inverse cosine and sine. The tutorial demonstrates how to isolate trigonometric functions, use inverse functions to find solutions, and apply the Pythagorean theorem to solve for unknowns. Each example is explained step-by-step, with calculations and approximations provided for clarity.

What is the first step in solving a trigonometric equation involving the sine function?

• Add 1 to both sides

• Subtract 1 from both sides

• Multiply both sides by 2

• Divide both sides by 2

What is the result of taking the inverse sine of 1/10?

• Approximately 1.1002

• Approximately 1.2001

• Approximately 0.2001

• Approximately 0.1002

How do you find the angle in the second quadrant with the same sine value as a given angle?

• Add the angle to π

• Divide the angle by 2

• Subtract the angle from π

• Multiply the angle by 2

What is the second solution for x in the equation involving sine?

• 3 - π - inverse sine of 1/10

• 3 - π + inverse sine of 1/10

• 3 + π - inverse sine of 1/10

• 3 + π + inverse sine of 1/10

What is the value of x when arctangent of x equals π/4?

• 0

• 1

• π

• π/2

In a 45-45-90 triangle, what is the ratio of the legs to the hypotenuse?

• 1:1:√2

• 1:√3:2

• 1:2:√3

• 1:1:2

What is the tangent of π/4 radians?

• 1

• 0

• √2

• π

What is the cosine of an angle whose sine is 3/7?

• 7/3

• √10/7

• 2√10/7

• 3/7

Which quadrant is the reference triangle located in when the sine value is positive?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

How do you solve for x in the equation inverse cosine of x equals inverse sine of 3/7?

• By taking the arctangent of both sides

• By taking the sine of both sides

• By taking the cosine of both sides

• By taking the tangent of both sides