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 how tangent equals sine over cosine. The Pythagorean identity is derived using the Pythagorean theorem, leading to three key identities. Cofunction identities are explored using the unit circle, showing relationships between complementary angles. The video concludes with a summary of the basic identities covered.

Which of the following is NOT a trigonometric function?

• Sine

• Cosine

• Logarithm

• Tangent

What is the reciprocal of sine?

• Cosine

• Cosecant

• Secant

• Tangent

How is tangent defined in terms of sine and cosine?

• Cosine times sine

• Sine times cosine

• Cosine over sine

• Sine over cosine

What is the reciprocal of tangent?

• Secant

• Cotangent

• Cosine

• Sine

What is the Pythagorean identity?

• tan²θ + 1 = sec²θ

• sinθ = cos(90° - θ)

• 1 + cot²θ = csc²θ

• sin²θ + cos²θ = 1

What does dividing the Pythagorean identity by cos²θ yield?

• tan²θ + 1 = sec²θ

• 1 + cot²θ = csc²θ

• sin²θ + cos²θ = 1

• sinθ = cos(90° - θ)

What does dividing the Pythagorean identity by sin²θ yield?

• sin²θ + cos²θ = 1

• sinθ = cos(90° - θ)

• 1 + cot²θ = csc²θ

• tan²θ + 1 = sec²θ

What is the sine of 30 degrees equal to in terms of cosine?

• cos(0°)

• cos(90°)

• cos(30°)

• cos(60°)

Which identity relates sine and cosine of complementary angles?

• secθ = csc(90° - θ)

• tanθ = cot(90° - θ)

• cosθ = sin(90° - θ)

• sinθ = cos(90° - θ)

Which identity relates tangent and cotangent of complementary angles?

• sinθ = cos(90° - θ)

• secθ = csc(90° - θ)

• cotθ = tan(90° - θ)

• tanθ = cot(90° - θ)