Trigonometric Identities and Functions

The video tutorial covers various trigonometric identities, starting with basic ones like sine, cosine, and tangent, and moving to more complex identities derived from the unit circle. It explains how to derive new identities by dividing basic formulas and discusses the concepts of even and odd functions. The tutorial also explores the unit circle's role in understanding periodicity and introduces sum and difference formulas, providing mnemonic aids for memorization.

Which of the following is the correct expression for cosecant?

• 1 over cosine

• 1 over sine

• Sine over cosine

• Cosine over sine

What is the fundamental trigonometric identity involving sine and cosine?

• Sine plus cosine equals one

• Sine times cosine equals one

• Sine squared plus cosine squared equals one

• Sine squared plus cosine squared equals zero

How can you derive the identity 1 + tangent squared equals secant squared?

• Divide the fundamental identity by cosine squared

• Subtract sine squared from the fundamental identity

• Multiply the fundamental identity by cosine squared

• Divide the fundamental identity by sine squared

What is the identity for sine of a negative angle?

• Sine of negative theta equals negative cosine of theta

• Sine of negative theta equals sine of theta

• Sine of negative theta equals cosine of theta

• Sine of negative theta equals negative sine of theta

Which function is symmetric about the y-axis?

• Cotangent

• Cosine

• Tangent

• Sine

What happens to the value of cosine when you add 2π to the angle?

• It doubles

• It becomes zero

• It remains the same

• It becomes negative

What is the identity for sine of theta plus 2π?

• Sine of theta plus 2π equals zero

• Sine of theta plus 2π equals sine of theta

• Sine of theta plus 2π equals cosine of theta

• Sine of theta plus 2π equals negative sine of theta

What mnemonic is used to remember the sine sum identity?

• Sine is something that stays

• Sine is something that subtracts

• Sine is something that switches

• Sine is something that adds

How does the cosine sum identity differ from the sine sum identity?

• Cosine stays the same

• Cosine subtracts terms

• Cosine switches signs

• Cosine adds terms

What is the result of cosine of X plus Y?

• Cosine X times cosine Y minus sine X times sine Y

• Cosine X times sine Y plus sine X times cosine Y

• Sine X times cosine Y plus cosine X times sine Y

• Sine X times sine Y minus cosine X times cosine Y