Trigonometric Functions and Equations

The video tutorial explains how to solve two trigonometric equations over the interval from 0 to 2π radians. The first equation, tangent x + 1 = 0, is solved by identifying angles in the second and fourth quadrants where the tangent is -1. The solutions are 3π/4 and 7π/4 radians. The second equation, cosecant x - 2 = 0, is solved by finding angles where the sine is 1/2, resulting in solutions at π/6 and 5π/6 radians. The tutorial uses the unit circle to find these solutions and provides a clear step-by-step approach.

What is the interval over which the trigonometric equations are solved in this tutorial?

• 0 to π

• 0 to 2π

• π to 2π

• 0 to 3π

What is the first step in solving the equation tangent x + 1 = 0?

• Add 1 to both sides

• Subtract 1 from both sides

• Multiply both sides by 2

• Divide both sides by 2

In which quadrants do we find solutions for tangent x = -1?

• First and Third

• Second and Fourth

• Third and Fourth

• First and Second

What is the angle in radians for the solution in the second quadrant for tangent x = -1?

• π/4

• 3π/4

• 5π/4

• 7π/4

What is the reciprocal of the sine function known as?

• Secant

• Cosecant

• Cotangent

• Cosine

What is the sine value when cosecant x equals 2?

• 1

• 1/2

• 2

• 0

In which quadrants is the y-coordinate positive on the unit circle?

• First and Fourth

• First and Second

• Second and Third

• Third and Fourth

What is the angle in radians for the first solution of sine x = 1/2?

• π/6

• π/3

• 2π/3

• 5π/6

What is the angle in radians for the second solution of sine x = 1/2?

• π/3

• π/6

• 2π/3

• 5π/6

What is the cosecant value when sine x equals 1/2?

• 1/2

• 1

• 2

• 3