Trigonometric Functions and Equations

This video tutorial focuses on solving various trigonometric equations. It begins with solving 2sin(x) + csc(x) = 0, which has no solution. Next, it addresses cos(x) - sin(x) = 0, leading to tangent solutions using the unit circle and triangles. The tutorial then explores solving 3tan^3(x) = tan(x) by factoring and finding general solutions. Finally, it covers solving 2sin^2(x) + 3sin(x) + 1 = 0 using substitution and factoring techniques.

What is the first step in solving the equation 2 sine x plus cosecant x equals 0?

• Add 1 to both sides

• Multiply both sides by sine x

• Subtract 1 from both sides

• Multiply both sides by cosine x

Why does the equation 2 sine x plus cosecant x equals 0 have no solution?

• Sine squared cannot be negative

• The equation is not quadratic

• Cosecant is undefined

• Sine x is always positive

What is the result when cosine x equals sine x?

• Tangent x equals 1

• Sine x equals 0

• Cosine x equals 0

• Tangent x equals 0

In which quadrants is tangent positive?

• Quadrants 1 and 2

• Quadrants 2 and 3

• Quadrants 3 and 4

• Quadrants 1 and 3

What is the reference angle for tangent x equals 1?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

What should you do first when solving 3 tan cube x equals tan x?

• Divide both sides by tan x

• Subtract tan x from both sides

• Add tan x to both sides

• Multiply both sides by tan x

At what angles is tangent x equal to zero?

• 0 and pi

• pi/6 and 5pi/6

• pi/2 and 3pi/2

• pi/4 and 3pi/4

Which triangle is used to find the reference angle for tangent x equals plus or minus root three over three?

• 90-90-90 triangle

• 60-60-60 triangle

• 45-45-90 triangle

• 30-60-90 triangle

What type of equation is 2 sine squared x plus three sine x plus one?

• Quadratic equation

• Linear equation

• Cubic equation

• Exponential equation

What is the reference angle for sine x equals negative one?

• 360 degrees

• 180 degrees

• 90 degrees

• 270 degrees