Trigonometric Functions and Angles

The video tutorial explains how to solve the trigonometric equation 2 sine theta + square root 3 = 0 within a given interval. It demonstrates two methods: using the unit circle and reference triangles. The unit circle method involves identifying points with specific sine values in the third and fourth quadrants, while the reference triangles method uses 30-60-90 triangles to find solutions. The video concludes by highlighting the importance of understanding both methods for solving trigonometric equations.

What is the first step in solving the equation 2 sine theta + square root 3 = 0?

• Add square root 3 to both sides

• Subtract square root 3 from both sides

• Multiply both sides by 2

• Divide both sides by 2

In which quadrants is the sine function negative?

• Second and Third

• Third and Fourth

• First and Second

• First and Fourth

What is the sine value of the angle 240 degrees on the unit circle?

• Square root 3 divided by 2

• -Square root 3 divided by 2

• -1/2

• 1/2

Which angle in the fourth quadrant has a sine value of -square root 3 divided by 2?

• 60 degrees

• 300 degrees

• 120 degrees

• 240 degrees

What type of triangle is used as a reference for solving the equation?

• 45-45-90 triangle

• Equilateral triangle

• Isosceles triangle

• 30-60-90 triangle

What is the sine of 60 degrees in a 30-60-90 triangle?

• Square root 3 divided by 2

• 1/2

• 1

• Square root 2 divided by 2

In the third quadrant, what are the signs of the x and y coordinates?

• X negative, Y positive

• Both positive

• X positive, Y negative

• Both negative

What is the solution in radians for the angle in the third quadrant?

• 2pi/3

• 5pi/3

• 4pi/3

• pi/3

What is the solution in radians for the angle in the fourth quadrant?

• 2pi/3

• 4pi/3

• pi/3

• 5pi/3

Which method can be used to solve trigonometric equations besides the unit circle?

• Graphing

• Calculus

• Reference triangles

• Algebraic manipulation