Trigonometric Functions and Angles

The video tutorial explains how to solve the equation cosine x equals square root two divided by two for all solutions, using reference triangles and the unit circle. It begins by identifying where cosine is positive on the coordinate plane, then finds the reference angle that gives the desired cosine value. The tutorial continues by determining coterminal angles and expressing all solutions in terms of radians. Finally, it verifies the solutions using the unit circle and a graph, demonstrating the infinite number of solutions due to the periodic nature of the cosine function.

What method is used to solve the equation cosine x equals square root two divided by two?

• Graphical method only

• Algebraic manipulation

• Numerical approximation

• Reference triangles and unit circle

In which quadrants is the cosine function positive?

• Second and third

• First and second

• Third and fourth

• First and fourth

What type of triangle is used to find the reference angle for cosine x equals square root two divided by two?

• 30-60-90 triangle

• Scalene triangle

• Equilateral triangle

• 45-45-90 triangle

What is the reference angle in radians for cosine x equals square root two divided by two?

• pi/6

• pi/3

• pi/2

• pi/4

How do you find all coterminal angles for a given angle?

• Subtract multiples of pi

• Add multiples of 2pi

• Add multiples of pi

• Subtract multiples of 2pi

What is the least positive angle in the fourth quadrant for cosine x equals square root two divided by two?

• pi/4

• 3pi/4

• 5pi/4

• 7pi/4

What is the general solution for angles in the first quadrant?

• x = pi/4 + 2pi k

• x = 3pi/4 + 2pi k

• x = 5pi/4 + 2pi k

• x = 7pi/4 + 2pi k

How is the solution verified using the unit circle?

• By checking the angle

• By checking the radius

• By checking the x-coordinate

• By checking the y-coordinate

What does the graph of y = cosine x and y = square root two divided by two show?

• No intersections

• Finite intersections

• One intersection

• Infinite intersections

What is the next angle in the positive direction after pi/4?

• 3pi/4

• 5pi/4

• 9pi/4

• 11pi/4