Solving Cosine Equations and Angles

The video tutorial explains how to solve the equation cosine x equals 0.45 within a specified interval. It highlights the use of the inverse cosine function to find solutions, as the unit circle or reference triangles are not applicable. The tutorial demonstrates using a calculator to determine the angle in radians and identifies solutions in both the first and fourth quadrants. It also covers calculating the second solution by subtracting the reference angle from 2π, ensuring accuracy by comparing rounded and precise values.

What is the primary method used to solve the equation cosine x = 0.45?

• Using a calculator and inverse cosine

• Using reference triangles

• Using the unit circle

• Using trigonometric identities

What is the range of the inverse cosine function?

• 0 to 2π radians

• -π/2 to π/2 radians

• 0 to π radians

• -π to π radians

Which mode should the calculator be in to find the angle for cosine x = 0.45?

• Degree mode

• Radian mode

• Gradian mode

• Decimal mode

What is the approximate value of the angle in radians for the first solution?

• 1.5708 radians

• 1.1040 radians

• 0.7854 radians

• 2.3562 radians

In which quadrant is the first solution located?

• First quadrant

• Fourth quadrant

• Second quadrant

• Third quadrant

What is the reference angle for the second solution in the fourth quadrant?

• 0.7854 radians

• 1.5708 radians

• 2.3562 radians

• 1.1040 radians

How do you calculate the second solution in the fourth quadrant?

• Subtract the reference angle from π

• Subtract the reference angle from 2π

• Add the reference angle to π

• Add the reference angle to 2π

What is the approximate value of the second solution in radians?

• 4.7124 radians

• 3.1416 radians

• 6.2832 radians

• 5.1792 radians

Why is there a second solution in the fourth quadrant?

• Cosine is positive in the first and fourth quadrants

• Cosine is negative in the first and fourth quadrants

• Cosine is zero in the first and fourth quadrants

• Cosine is undefined in the first and fourth quadrants

What is the significance of the reference triangle in solving the equation?

• It helps in visualizing the angle

• It is used to calculate sine values

• It is irrelevant to the solution

• It provides the exact angle measurement