Trigonometric Identities and Properties

The video tutorial covers the application of Pythagorean identities in trigonometry, focusing on simplifying expressions involving trigonometric functions squared. The instructor explains how to recognize when to use these identities and demonstrates transforming and simplifying expressions. The tutorial also covers simplifying complex fractions by using reciprocal multiplication, providing a step-by-step approach to solving trigonometric problems.

What should you immediately consider when you see a trigonometric function squared?

• Find the derivative

• Use the quadratic formula

• Calculate the integral

• Apply the Pythagorean identities

Which identity is used for sine squared and cosine squared?

• cosine squared of x plus secant squared of x equals one

• tangent squared of x plus cotangent squared of x equals one

• sine squared of x plus cosine squared of x equals one

• sine squared of x plus tangent squared of x equals one

What is the identity for cosecant squared in terms of cotangent?

• One plus sine squared of x equals cosecant squared of x

• One plus secant squared of x equals cosecant squared of x

• One plus cotangent squared of x equals cosecant squared of x

• One plus tangent squared of x equals cosecant squared of x

How can you transform the identity sine squared of x plus cosine squared of x equals one to fit 1 minus sine squared of x?

• Add sine squared of x to both sides

• Subtract sine squared of x from both sides

• Multiply both sides by sine squared of x

• Divide both sides by cosine squared of x

What property is used when subtracting the same term from both sides of an equation?

• Addition property of equality

• Subtraction property of equality

• Multiplication property of equality

• Division property of equality

What is the next step after replacing terms with their equivalents in an expression?

• Simplify the expression further

• Add a constant to both sides

• Divide by a constant

• Multiply by a random number

What identity is used to express cotangent squared in terms of sine and cosine?

• Cotangent squared equals tangent squared over sine squared

• Cotangent squared equals cosine squared over tangent squared

• Cotangent squared equals sine squared over cosine squared

• Cotangent squared equals cosine squared over sine squared

How do you eliminate a fraction in the denominator of a fraction?

• Divide the numerator by the fraction

• Subtract the fraction from the numerator

• Multiply by the reciprocal of the denominator

• Add the same fraction to the numerator

What happens when you multiply a number by its reciprocal?

• The result is zero

• The result is the reciprocal

• The result is one

• The result is the original number

What is the final result when cosine squared in the numerator and denominator are divided out?

• One

• Zero

• Sine squared

• Cosine squared