1. Trigonometry Lesson 3 Aims:
• To know and learn 3 special trig identities.
• To be able to prove various trig identities
• To be able to solve angle problems by using Pythagoras
rule and using the trig identities.

2. Trigonometric identities
Earlier in the course you met the following trigonometric identities:
We can rearrange these to give the identities in terms of sec θ, cosec θ and cot θ below!
If necessary, remind students of the difference between an equation and an identity.

3. Problems involving reciprocal trig functions
Given that x is an acute angle and tan x = find the exact values of cot x, sec x and cosec x.
Using the identities:
Using a right-angled triangle, we could define sec x as hypotenuse/adjacent, cosec x as hypotenuse/opposite and cot x as adjacent/opposite.
Therefore
cot x =
sec x =
cosec x =

4. Problems involving reciprocal trig functions
Given that x is an acute angle and tan x = find the exact values of cot x, sec x and cosec x.
An alternative method!
Using the following right-angled triangle:
The length of the hypotenuse is x So
tan x =
cos x =
sin x =
Using a right-angled triangle, we could define sec x as hypotenuse/adjacent, cosec x as hypotenuse/opposite and cot x as adjacent/opposite.
Therefore
cot x =
sec x =
cosec x =

5. Problems involving reciprocal trig functions
Given that cos B = is an obtuse angle . Find cot B.
Making use of the identity :
We chose the –ve square root because the angle is obtuse and the graph is negative between 90 and 180.
Using a right-angled triangle, we could define sec x as hypotenuse/adjacent, cosec x as hypotenuse/opposite and cot x as adjacent/opposite.

6. Problems involving reciprocal trig functions
Given that cos B = is an obtuse angle . Find cot B.
Draw a right-angled triangle with cos B = :
The missing length is B So
tan B =
Therefore
Using a right-angled triangle, we could define sec x as hypotenuse/adjacent, cosec x as hypotenuse/opposite and cot x as adjacent/opposite.
cot B =

7. On W/b – choose your favoured method
Given that x is an acute angle and cos x = find the exact values of sec x, cosec x and cot x
Using a right-angled triangle, we could define sec x as hypotenuse/adjacent, cosec x as hypotenuse/opposite and cot x as adjacent/opposite.
cosec x =
sec x =
cot x =
Do Exercise B, page 57,qu 9 & 10

8. On W/b – choose your favoured method
Given that x is an obtuse angle and cos x = find the exact values of sec x, cosec x and cot x
Using a right-angled triangle, we could define sec x as hypotenuse/adjacent, cosec x as hypotenuse/opposite and cot x as adjacent/opposite.
cosec x =
sec x =
cot x =
Do Exercise B, page 57,qu 9 & 10

9. Problems involving reciprocal trig functions
Trig match puzzle
Prove that
At home do Exercise B, qu’s 5,6 & 7
Using sin2x + cos2x = 1
Explain that this identity can be proved by rearranging the left-hand side (LHS) to give the right-hand side (RHS).