Trigonometric Equations and Identities

The video tutorial covers solving trigonometric equations, starting with isolating single trig functions and using the unit circle to find solutions. It progresses to solving equations involving cosecant and mixed trig functions, employing techniques like factoring and using the quadratic formula. The tutorial also addresses handling extraneous solutions and concludes with practice problems to reinforce learning.

What is the first step in solving a trigonometric equation with a single trig function?

• Square both sides

• Isolate the trig function

• Use the quadratic formula

• Factor the equation

When solving for sine squared equals one fourth, what is the next step after isolating sine squared?

• Add 1 to both sides

• Subtract 1 from both sides

• Multiply by 4

• Take the square root of both sides

What is the reciprocal of cosecant?

• Sine

• Tangent

• Secant

• Cosine

In which quadrants do you find solutions for sine equals plus or minus rad 3 over 2?

• Quadrants 1 and 2

• Quadrants 2 and 3

• All four quadrants

• Quadrants 3 and 4

What should you do if a trigonometric equation has more than one trig function?

• Isolate one trig function

• Factor the equation

• Use a trig identity to change one function

• Square both sides

Where does sine equal 1 on the unit circle?

• 3 Pi over 2

• Pi

• 2 Pi

• Pi over 2

What is the first step in factoring a quadratic-like trigonometric equation?

• Isolate the trig function

• Identify the squared and linear terms

• Square both sides

• Use the quadratic formula

What is the highest value that sine can reach?

• 1

• 2

• 0.5

• Infinity

What should you do if a trigonometric equation involves different trig functions and nothing is squared?

• Factor the equation

• Use the quadratic formula

• Square both sides

• Isolate one trig function

Why is it necessary to check for extraneous solutions when squaring both sides of an equation?

• To ensure the equation is factored correctly

• To verify the unit circle values

• Because squaring can introduce false solutions

• To simplify the equation