Trigonometric Identities and Functions

Professor Dave introduces trigonometric identities, starting with the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. He explains reciprocal identities and the tangent identity, followed by the derivation of the Pythagorean identity. The video also covers cofunction identities using the unit circle. The session concludes with a summary and a comprehension check.

Which of the following is NOT a trigonometric function?

• Logarithm

• Cosine

• Tangent

• Sine

What is the reciprocal of the sine function?

• Secant

• Cosecant

• Cotangent

• Tangent

How is tangent expressed in terms of sine and cosine?

• Cosine times sine

• Sine times cosine

• Cosine over sine

• Sine over cosine

What is the identity for cotangent in terms of sine and cosine?

• Sine over cosine

• Cosine over sine

• Sine times cosine

• Cosine times sine

Which identity is derived from the Pythagorean theorem?

• All of the above

• Tangent squared plus one equals secant squared

• Sine squared plus cosine squared equals one

• One plus cotangent squared equals cosecant squared

What does dividing the Pythagorean identity by cosine squared theta yield?

• Tangent squared plus one equals secant squared

• Sine squared plus cosine squared equals one

• One plus cotangent squared equals cosecant squared

• Sine over cosine equals tangent

What is the cofunction identity for sine?

• Sine of theta equals cosine of ninety minus theta

• Cosine of theta equals sine of ninety minus theta

• Tangent of theta equals cotangent of ninety minus theta

• Secant of theta equals cosecant of ninety minus theta

Which angle pair demonstrates the cofunction identity for cosine?

• Sine of thirty and cosine of sixty

• Cosine of zero and sine of ninety

• Tangent of forty-five and cotangent of forty-five

• Secant of thirty and cosecant of sixty

What is the relationship between tangent and cotangent in cofunction identities?

• Tangent of theta equals cotangent of ninety minus theta

• Cotangent of theta equals cosine of ninety minus theta

• Cotangent of theta equals tangent of ninety minus theta

• Tangent of theta equals sine of ninety minus theta

Which identity is crucial for understanding complementary angles?

• Quotient identities

• Cofunction identities

• Pythagorean identities

• Reciprocal identities