Trigonometric Equations and Solving Methods

This video tutorial covers trigonometric equations, starting with simple equations and progressing to those involving squared trigonometric functions. It explains how to solve equations like 3 tan x = 1 and 2 cos²x = 1, and introduces methods for handling quadratic trigonometric equations. The tutorial provides step-by-step solutions and graphical interpretations to help understand the concepts.

What is the first step in solving the equation 3 tan x = 1 for x in the range 0 to 270 degrees?

• Divide both sides by 3

• Subtract 3 from both sides

• Multiply both sides by 3

• Add 3 to both sides

When solving 2 cos squared x = 1, what is the value of cos x after taking the square root of both sides?

• 1

• Root 2

• 1/2

• Plus or minus 1 over root 2

What is the second solution for cos x = 1 over root 2 due to symmetry?

• 90 degrees

• -45 degrees

• 225 degrees

• 135 degrees

Which of the following is a solution for cos x = -1 over root 2?

• 0 degrees

• 90 degrees

• 135 degrees

• 45 degrees

What is the factorized form of the quadratic equation 2 sin squared x - sin x - 1 = 0?

• (2 sin x + 1)(2 sin x - 1)

• (2 sin x - 1)(sin x + 1)

• (2 sin x + 1)(sin x - 1)

• (sin x - 1)(sin x + 1)

What is the solution for sin x = 1 within the range 0 to 360 degrees?

• 180 degrees

• 270 degrees

• 90 degrees

• 0 degrees

For the equation 2 sin squared x - sin x = 1, what are the solutions for sin x = -1/2?

• 30 degrees and 150 degrees

• 90 degrees and 270 degrees

• 0 degrees and 180 degrees

• 210 degrees and 330 degrees