Master Solving for all of the solutions for trigonometric equations using inverse operations

The video tutorial explains how to solve trigonometric equations using inverse operations and the unit circle. It covers isolating trigonometric functions, using inverse trigonometric functions, and finding all solutions by considering coterminal angles. The tutorial also addresses solving equations involving sine, cosine, and tangent, as well as reciprocal functions like secant and cosecant. The instructor provides step-by-step examples to illustrate these concepts.

What is the first step in solving a trigonometric equation using inverse operations?

• Multiply both sides by a constant

• Isolate the trigonometric function

• Use the unit circle directly

• Add a constant to both sides

In which quadrants is the tangent function negative?

• 1st and 3rd

• 3rd and 4th

• 2nd and 4th

• 1st and 2nd

What is the angle in the 4th quadrant where tangent equals -√3?

• π/3

• 4π/3

• 2π/3

• 5π/3

When is the sine function negative?

• 3rd and 4th quadrants

• 2nd and 3rd quadrants

• 1st and 4th quadrants

• 1st and 2nd quadrants

What are the angles where sine equals -√2/2?

• 5π/4 and 7π/4

• π/2 and 3π/2

• π/4 and 3π/4

• π and 2π

How should you handle reciprocal trigonometric functions?

• Ignore them in calculations

• Use a calculator to solve them

• Use them directly without modification

• Convert them to sine, cosine, or tangent

What is the reciprocal of secant?

• Cosecant

• Sine

• Cosine

• Tangent

What is the first step in solving a complex trigonometric equation?

• Directly solve using a calculator

• Multiply all terms by a constant

• Add all terms to one side

• Use inverse operations to simplify

What is the solution for cotangent squared of X equals 1/3?

• X = ±√3

• X = ±2

• X = ±1/√3

• X = ±1/2

How do you find all solutions for a trigonometric equation?

• Subtract 2π from each solution

• Subtract π from each solution

• Add 2π to each solution

• Add π to each solution