Find all the solutions of trig equation with cotangent

The video tutorial guides students through solving trigonometric equations by using substitutions and simplifications. It emphasizes understanding the notation and algebra involved, and finding all possible solutions, including those within a specific range. The teacher provides step-by-step instructions and clarifies common misconceptions, ensuring students grasp the concepts of trigonometric identities and their applications.

What is the first step in solving the equation X^2 = 3?

• Multiply both sides by 2

• Take the square root of both sides

• Subtract 3 from both sides

• Add 3 to both sides

Why can't you multiply by 4 until the expression is outside the radical?

• It changes the equation's balance

• It makes the equation unsolvable

• It violates mathematical rules

• It doesn't affect the equation

Why is it beneficial to substitute cotangent with tangent in trigonometric equations?

• Tangent is easier to spell

• Tangent is more commonly used

• Tangent simplifies the calculation by using reciprocal relationships

• Tangent has fewer variables

What is the relationship between angles that are equidistant from each other?

• They are always 45 degrees apart

• They are multiples of 2π apart

• They are always 90 degrees apart

• They are multiples of π apart

How many solutions are expected between 0 and 2π for the given trigonometric equation?

• 4 solutions

• 8 solutions

• 2 solutions

• 6 solutions

What is the significance of the angle π/12 in the context of the problem?

• It is irrelevant to the problem

• It is the smallest angle in the unit circle

• It is the largest angle in the unit circle

• It is used to find additional solutions within the range

What happens to the number of X-intercepts when the tangent graph is compressed?

• The number of X-intercepts decreases

• The number of X-intercepts remains the same

• The number of X-intercepts increases

• The number of X-intercepts becomes zero