Solving Trigonometric Equations Challenge

The video tutorial covers solving trigonometric equations using algebraic methods and trigonometric identities. It provides examples of solving equations involving cosine, sine, and tangent, emphasizing the use of the unit circle, reference angles, and periodic functions. The tutorial also highlights the importance of recognizing when equations have no solutions.

What is the reference angle for a cosine value of square root of 3 over 2?

• 30 degrees (PI/6)

• 45 degrees (PI/4)

• 60 degrees (PI/3)

• 90 degrees (PI/2)

In which quadrants is the cosine positive?

• Quadrant I and IV

• Quadrant III and IV

• Quadrant I and II

• Quadrant II and III

What is the sine of PI/3?

• 1/2

• square root of 3 over 2

• square root of 2 over 2

• 1

Which quadrants have a positive sine value?

• III and IV

• II and III

• I and II

• I and IV

How is the tangent function related to sine and cosine?

• tangent = cosine / sine

• tangent = sine / cosine

• tangent = sine + cosine

• tangent = sine * cosine

What is the reference angle for a tangent of square root of 3 over 3?

• 90 degrees (PI/2)

• 30 degrees (PI/6)

• 45 degrees (PI/4)

• 60 degrees (PI/3)

When does the cosine function have no solution?

• cosine = 1/2

• cosine = 1

• cosine = 0

• cosine = -3

What is the double angle identity for sine?

• sin(2x) = sin(x) * sin(x)

• sin(2x) = 2 sin(x) / cos(x)

• sin(2x) = sin(x) + cos(x)

• sin(2x) = 2 sin(x) cos(x)

What is the result when cosine of X is zero?

• X = PI/6, 5PI/6

• X = PI/4, 3PI/4

• X = 0, PI

• X = PI/2, 3PI/2

How do you find all possible solutions for trigonometric functions?

• Add 2PI K to each solution

• Divide each solution by 2PI

• Subtract 2PI from each solution

• Multiply each solution by 2PI