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.

Tags

CCSS.8.EE.C.7A

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)

Tags

CCSS.HSF.TF.A.4

What is the reciprocal of sin(θ)?

• sec(θ)

• tan(θ)

• cos(θ)

• cosec(θ)

Tags

CCSS.HSF.TF.A.2

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

• sin(θ)

• cot(θ)

• cos(θ)

• tan(θ)

Tags

CCSS.HSG.SRT.C.6

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)

Tags

CCSS.HSF.TF.C.8

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

Tags

CCSS.HSF.TF.A.2

What is the value of cos(90 degrees)?

• 0

• 1

• Infinity

• Undefined

Tags

CCSS.HSF.TF.A.2

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)

Tags

CCSS.HSF.TF.C.8

What does 'co' in cos(θ) stand for?

• Complement

• Coordinate

• Coefficient

• Constant

Tags

CCSS.HSF.TF.A.2

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

• b/a

• a/b

• 1/a

• 1/b

Tags

CCSS.HSG.SRT.C.7