Master Simplifying rational trigonometric expressions

The video tutorial explains how to simplify rational trigonometric expressions by eliminating fractions and finding common denominators. It covers several examples using trigonometric functions like cosecant, secant, tangent, sine, and cosine. The tutorial emphasizes the use of trigonometric identities, particularly Pythagorean identities, to simplify expressions effectively.

What is the first step in simplifying rational trigonometric expressions?

• Use the quadratic formula

• Find the derivative

• Convert to radians

• Eliminate fractions

When adding fractions with different denominators, what must you find?

• Least common denominator

• Sum of the numerators

• Average of the denominators

• Greatest common factor

In the first example, what is the common denominator for cosecant and secant?

• Product of the functions

• Difference of the functions

• Sum of the functions

• Quotient of the functions

What is the benefit of converting trigonometric functions to sines and cosines?

• It simplifies the expression

• It makes differentiation easier

• It changes the angle

• It eliminates the need for a calculator

In the second example, what is the LCD for tangent and cosine?

• Sum of the denominators

• Product of the denominators

• Difference of the denominators

• Quotient of the denominators

What identity is used to simplify sine squared plus cosine squared?

• Double angle identity

• Half angle identity

• Pythagorean identity

• Sum of angles identity

In the third example, what property is used to expand expressions?

• Commutative property

• Identity property

• Associative property

• Distributive property

What is the result of factoring out a common term in an expression?

• It increases the degree of the polynomial

• It eliminates the constant term

• It simplifies the expression

• It changes the variable

In the final example, how is sine squared rewritten using Pythagorean identities?

• 1 - cosine squared

• cosine squared + 1

• 1 + cosine squared

• cosine squared - 1

What is the final simplified expression in the last example?

• Tangent of X

• Sine of X

• Secant of X

• Cosine of X