Trigonometric Limits 1

The video tutorial covers trigonometric limits, focusing on sine, cosine, and tangent functions. It explains the limit of sine of X over X as X approaches zero, and how to handle similar limits involving tangent and cosine. The tutorial also discusses the use of trigonometric identities and the concept of multiplying by a 'fancy one' to simplify limit problems.

Which of the following is a reciprocal of sine(x)?

• Secant(x)

• Tangent(x)

• Cosecant(x)

• Cosine(x)

What is the limit of sine(x)/x as x approaches zero?

• 0

• 1

• Undefined

• Infinity

In the expression 3 * sine(x)/x, what happens to the constant 3 when evaluating the limit as x approaches zero?

• It becomes zero

• It is multiplied by the limit of sine(x)/x

• It is divided by the limit of sine(x)/x

• It is ignored

How can tangent(x) be expressed using sine and cosine?

• sine(x) / cosine(x)

• cosine(x) / sine(x)

• 1 / sine(x)

• sine(x) * cosine(x)

What is the limit of tangent(x)/x as x approaches zero?

• Undefined

• 1

• 0

• Infinity

When dealing with sine(nx)/x, what must be true for the limit to equal 1 as x approaches zero?

• n must be zero

• n must equal the coefficient of x in the denominator

• n must be greater than the coefficient of x in the denominator

• n must be less than the coefficient of x in the denominator

What is a 'fancy one' in the context of limits?

• A method to simplify expressions

• A method to add constants

• A technique to multiply by 1 in a useful form

• A way to divide by zero

What is the purpose of multiplying by the conjugate in expressions like 1 - cosine(x)?

• To simplify the expression

• To eliminate the denominator

• To change the limit

• To add a constant

What trigonometric identity is used to simplify 1 - cosine(x)?

• tangent(x) = sine(x)/cosine(x)

• sine^2(x) + cosine^2(x) = 1

• cosine^2(x) = 1 - sine^2(x)

• sine(x) = 1/cosecant(x)

What is the limit of (1 - cosine(x))/x as x approaches zero?

• Undefined

• 0

• 1

• Infinity