4.4 Highlights

Question 1

The tangent of an angle θ, denoted tan θ, is defined by

Answer 1

tan θ = (sin θ) / (cos θ)

provided that cos θ does not equal 0

Question 2

Tan θ is the ___ of the radius of the unit circle corresponding to 0

sin θ and cos θ are the ____

Answer 2

slope

endpoints of the radius

Question 3

Provide the domain and range of:
Cosine
Sine
Tangent

Answer 3

Domain | Range
Cosine: (−∞,∞) | [−1, 1]
Sine: (−∞,∞) | [−1, 1]
Tangent: real numbers that are not odd multiples of π/2 | (−∞,∞)

Question 4

Secant of angle θ, denoted __ is defined by

Answer 4

sec θ = 1 / (cos θ)

Question 5

Cosecant of angle θ, denoted ___ is defined by

Answer 5

csc θ = 1/(sinθ)

Question 6

Cotangent of angle θ, denoted ___ is defined by

Answer 6

cot θ = (cosθ)/(sinθ)

Question 7

Prove how tangent and cotangent are multiplicative inverses

Answer 7

where tan θ and cot θ are both defined,

cot θ = 1 / tanθ