Trigonometric Functions and Angles

The video tutorial explains how to solve the trigonometric equation 4 cosine theta + 2 = 0 within the interval from 0 to 2PI. It begins by isolating cosine theta and identifying the quadrants where cosine is negative. The tutorial then explores two methods for finding solutions: using the unit circle and reference triangles. The unit circle method involves identifying points with an x-coordinate of -1/2, while the reference triangles method uses 30-60-90 triangles to verify solutions. The video concludes by emphasizing the importance of understanding both methods.

What is the first step in solving the equation 4cos(θ) + 2 = 0?

• Divide both sides by 4

• Multiply both sides by 4

• Subtract 2 from both sides

• Add 2 to both sides

In which quadrants is the cosine function negative?

• Second and Third

• First and Second

• First and Fourth

• Third and Fourth

What is the cosine value of the angle 2π/3 radians?

• -1

• 0

• -1/2

• 1/2

Which angle in the third quadrant has a cosine value of -1/2?

• 5π/3 radians

• π/3 radians

• 4π/3 radians

• 2π/3 radians

What is the reference angle for a cosine value of 1/2?

• π/6 radians

• π/4 radians

• π/3 radians

• π/2 radians

In a 30-60-90 triangle, what is the ratio of the adjacent side to the hypotenuse?

• 1/2

• √3/2

• 1

• √2/2

Which quadrant has both x and y coordinates negative?

• Fourth

• Second

• Third

• First

What is the cosine value of an angle in the second quadrant with a reference angle of π/3?

• -√3/2

• √3/2

• -1/2

• 1/2

What is the importance of using both the unit circle and reference triangles?

• To find new solutions

• To avoid using radians

• To verify solutions

• To simplify calculations

What is the final solution for θ in radians for the equation 4cos(θ) + 2 = 0?

• π/3 and 5π/3

• 2π/3 and 4π/3

• π/6 and 11π/6

• π/4 and 7π/4