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. Trigonometry Lesson 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!

Given that x is an acute angle and tan x = find the exact values of cot x, sec x and cosec x. Problems involving reciprocal trig functions Using the identities: Therefore cot x = sec x =cosec x =

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

Given that cos B = is an obtuse angle. Find cot B. Problems involving reciprocal trig functions 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.

Given that cos B = is an obtuse angle. Find cot B. Problems involving reciprocal trig functions Draw a right-angled triangle with cos B = : The missing length is So tan B = Therefore cot B = B

Given that x is an acute angle and cos x = find the exact values of sec x, cosec x and cot x On W/b – choose your favoured method cot x = sec x = cosec x = Do Exercise B, page 57,qu 9 & 10

Prove that Problems involving reciprocal trig functions Using sin 2 x + cos 2 x = 1 At home do Exercise B, qu’s 5,6 & 7 Trig match puzzle