Exploring Trigonometric Identities: Reciprocals, Ratios & Complements

The video tutorial covers trigonometric identities, explaining their nature and how they differ from equations. It introduces reciprocal identities like sec, cosec, and cot, and discusses ratio identities involving tan, cos, and sin. The tutorial also explores complementary identities, emphasizing their significance in trigonometry.

What makes an identity different from an equation?

• Identities are true for negative values.

• Identities are only true for positive values.

• Identities are true for all values.

• Identities are true for specific values.

Which of the following is a reciprocal identity?

• tan(θ) = 1/sin(θ)

• sec(θ) = 1/cos(θ)

• sin(θ) = 1/cos(θ)

• cot(θ) = 1/cos(θ)

What is the reciprocal of sin(θ)?

• sec(θ)

• tan(θ)

• cos(θ)

• cosec(θ)

Which trigonometric function is defined as opposite over adjacent in a right-angled triangle?

• sin(θ)

• cot(θ)

• cos(θ)

• tan(θ)

What is tan(θ) in terms of sin(θ) and cos(θ)?

• 1/cos(θ)

• 1/sin(θ)

• cos(θ)/sin(θ)

• sin(θ)/cos(θ)

At which angles does tan(θ) not exist within the 0 to 360-degree domain?

• 45 and 135 degrees

• 90 and 270 degrees

• 60 and 300 degrees

• 0 and 180 degrees

What is the value of cos(90 degrees)?

• 0

• 1

• Infinity

• Undefined

Which trigonometric functions are complementary?

• sin(θ) and tan(θ)

• cos(θ) and cot(θ)

• tan(θ) and sec(θ)

• sin(θ) and cos(θ)

What does 'co' in cos(θ) stand for?

• Complement

• Coordinate

• Coefficient

• Constant

In a right-angled triangle, if sin(θ) = a/b, what is cos(90 - θ)?

• b/a

• a/b

• 1/a

• 1/b