Trigonometric Functions and Angles

The video tutorial explains how to solve the trigonometric equation sine x + 1/2 = 0 within a given interval. It covers two main methods: using the unit circle and reference triangles. The unit circle method involves identifying angles with a sine value of -1/2 in the third and fourth quadrants, leading to solutions at 210 degrees and 330 degrees. The reference triangle method uses a 30-degree reference angle to find the same solutions. The tutorial also discusses finding all possible solutions by considering coterminal angles. The importance of understanding different solving methods is emphasized.

What is the first step in solving the equation sine x + 1/2 = 0?

• Multiply both sides by 2

• Divide both sides by sine

• Add 1/2 to both sides

• Subtract 1/2 from both sides

Which quadrants should be considered when looking for angles with a sine value of -1/2 using the unit circle?

• First and second quadrants

• Second and third quadrants

• Third and fourth quadrants

• First and fourth quadrants

Which method involves using the y-coordinate on the unit circle to find sine values?

• Reference triangles method

• Unit circle method

• Graphical method

• Algebraic method

What is the sine value of a 30-degree reference angle?

• -1/2

• 1/2

• 0

• 1

In which quadrants is the sine function negative?

• First and fourth

• First and second

• Second and third

• Third and fourth

What is the reference angle used in the reference triangles method for solving sine x = -1/2?

• 45 degrees

• 60 degrees

• 30 degrees

• 90 degrees

What is the significance of a 30-60-90 triangle in solving sine x = -1/2?

• It is used to find cosine values

• It helps identify the reference angle

• It is irrelevant to the problem

• It is used to find tangent values

How can you express all solutions for the angle 210 degrees?

• X = 210 degrees + 270 degrees x K

• X = 210 degrees + 90 degrees x K

• X = 210 degrees + 360 degrees x K

• X = 210 degrees + 180 degrees x K

What is the general expression for angles coterminal with 330 degrees?

• X = 330 degrees + 270 degrees x K

• X = 330 degrees + 90 degrees x K

• X = 330 degrees + 360 degrees x K

• X = 330 degrees + 180 degrees x K

What is the importance of recognizing different methods for determining angles with specific sine values?

• It is not necessary for understanding trigonometry

• It provides multiple approaches to solve trigonometric equations

• It helps in solving only simple equations

• It is only useful for academic purposes