Trigonometric Identities C3 Flashcards
sec(x)
1/[cos x]
cosec (x)
cot x
1/[tan x]
Draw graph of sec x
goes from 1 –> infinity
Draw graph of cosec x
Same as graph of sec x but (1 to inf, -inf to -1 to -inf, inf to 1 to inf..) but asymptote at x = 0, x = 180, with y=1 at x = 90
Draw graph of cot x
Vertical asymptotes at x = 180n (where sin x = 0), and repeats itself every 180 degrees.
Identity linking sin, cos
Identity linking tan, sec
Identity linking cot, cosec
1 + cot2x = cosec2x
Sketch arcsin(x).
What is the domain and range
- 1 ≤ x ≤ 1
- pi/2 ≤ arcsin x ≤ pi/2
Sketch arccos(x)
Domain?
Range?
-1 ≤ x ≤ 1
0 ≤ arccos x ≤ pi
Sketch arctan(x)
Domain ?
Range?
x e R
-pi/2 ≤ arctan x ≤ pi/2
sin(A±B)
sin A cos B ± cos
cos(A±B)
tan(A+B)
[tan A ± tan B]/[1 ∓ tan A tan B]
sin 2A
sin 2A = 2 sin A cos A
cos 2A
cos 2A = cos2A - sin2A
= 2cos 2A - 1
= 1 - 2sin2A
tan 2A
sin P + sin Q
2 sin[(P±Q)/2] cos [(P∓Q)/2]
cos P + cos Q
2cos[(P+Q)/2]cos[(P-Q)/2]
cos P - cos Q
-2sin[(P+Q)/2]sin[(P-Q)/2]
2 sin A cos B
sin[A+B] cos[A-B]
How would you convert these products into sums?
2 sin A cos B
2 cos A sin B
2 cos A cos B
2 sin A sin B
USE FACTOR FORMULA BUT REDEFINE VARIABLES SO THE ‘Product side’ is the neat variables.