6: Trig functions

Question 1

Secant, cosecant and cotangent are known as the reciprocal trig functions. Define each one in terms of cos, sin and tan.

Answer 1

Question 2

Write cot x in terms of cos x and sin x.

Answer 2

cot x = cos x / sin x

Question 3

What does it mean when you are asked to give the sign of a trig ratio?

Answer 3

State whether +ve or -ve

Question 4

Draw the graph of y = sec x

Answer 4

Question 5

Give the domain of y = sec x.

Answer 5

X ≠ any odd multiple of 90^o

Question 6

Draw the graph of y = cosec x

Answer 6

Question 7

Give the domain of y = cosec x

Answer 7

x ≠ any multiple of 180^o

Question 8

Draw the graph of y = cot x

Answer 8

Question 9

Give the domain of y = cot x

Answer 9

x ≠ any multiple of 180^o

Question 10

Use the identity sin²θ + cos²θ = 1 to produce:

• one involving tan and sec
• one involving cot and cosec

Answer 10

1. Divide by cos²θ: 1 + tan²θ = sec²θ
2. Divide by sin²θ: 1 + cot²θ = cosec²θ