Trigonometric Functions and Inverses

The video tutorial explains how to solve a trigonometric equation involving cosine on the interval from 0 to 2π. It begins by isolating the cosine function and determining the angles with a cosine value of -0.85. The tutorial uses a calculator to find solutions in radians, identifying angles in the second and third quadrants. It calculates the reference angle and verifies the solutions by checking cosine values.

What is the first step in solving the given trigonometric equation?

• Convert to degrees

• Multiply both sides by 2

• Add 0.85 to both sides

• Isolate the cosine function

In which quadrants is the cosine value negative?

• First and fourth

• Third and fourth

• Second and third

• First and second

What tool is necessary to find the inverse cosine of -0.85?

• Compass

• Ruler

• Calculator

• Protractor

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

• 4.712

• 1.234

• 2.587

• 3.142

How do you calculate the reference angle for the second solution?

• Divide 2.587 by pi

• Multiply 2.587 by pi

• Subtract 2.587 from pi

• Add 2.587 to pi

What is the approximate reference angle in radians?

• 0.555

• 1.570

• 2.000

• 3.142

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

• 3.697

• 4.712

• 3.142

• 2.587

How can you verify the solutions found for the equation?

• By checking with a calculator

• By using a protractor

• By using a ruler

• By drawing a unit circle

What should the cosine of 2.587 radians approximately equal?

• -0.5

• 0.5

• -0.85

• 0.85

What should the cosine of 3.697 radians approximately equal?

• 0.5

• 0.85

• -0.5

• -0.85