Understanding Radian Solutions in Trigonometric Equations

The video tutorial explains how to find the smallest three positive radian solutions for the equation 5 cosine 3 theta = 3. It begins by substituting 3 theta with U, solving for U using the cosine function, and employing a calculator to find the solutions. The tutorial covers finding solutions in the first and fourth quadrants, converting these solutions from U to theta, and ensuring accuracy by rounding appropriately. The process concludes with a summary of the solutions in terms of theta.

What is the initial substitution made to simplify the equation 5 cosine 3 theta = 3?

• U = 5 theta

• U = 3 theta

• U = theta / 3

• U = theta + 3

How do we isolate cosine U in the equation 5 cosine U = 3?

• Subtract 3 from both sides

• Multiply both sides by 5

• Divide both sides by 5

• Add 5 to both sides

Which mode should the calculator be in to find the inverse cosine of 3/5?

• Gradient mode

• Radian mode

• Degree mode

• Decimal mode

In which quadrants is the cosine function positive?

• First and fourth quadrants

• Third and fourth quadrants

• First and second quadrants

• Second and third quadrants

What is the approximate value of the first solution for U?

• 1.5708

• 2.3562

• 0.9273

• 3.1416

How is the second solution for U determined?

• By adding 2π to the first solution

• By dividing the first solution by 2

• By multiplying the first solution by 2

• By subtracting the reference angle from 2π

What is the approximate value of the second solution for U?

• 3.1416

• 4.7124

• 6.2832

• 5.3559

How is the third solution for U calculated?

• By dividing the second solution by 2

• By multiplying the second solution by 2

• By adding the reference angle to 2π

• By subtracting 2π from the first solution

What operation is performed to convert U to theta?

• Multiply U by 3

• Add 3 to U

• Subtract 3 from U

• Divide U by 3

What is the approximate value of theta sub 1?

• 0.927

• 0.309

• 2.404

• 1.785