Here’s a summary of Trigonometry for O Level Additional Mathematics. I go through what’s tested in this article here.
Assumed Trigonometry Knowledge for O Level Add Math:
For right angle triangles:
- sin x = opposite/ hypotenuse
- cos x = adjacent/ hypotenuse
- tan x = opposite/ adjacent
- Pythagoras Theorem: (hypotenuse)2 = (opposite)2 + (adjacent)2
For non- right angle triangles, you will use sine rule and cosine rule. These are found in the formula booklet of your exam, so don’t memorize them (just know where they are).
- sine rule:
- a/sin∠A = b/sin∠B = c/sin∠C
- cosine rule:
- c2 = a2+ b2 – 2abcos∠C
These are some trigonometric ratios that you are expected to know (note: they are not in you data booklet, so make sure you know them!)
cosec x = 1/ sin x
sec x = 1/ cos x
cot x = 1/ cot x
tan x = sinx / cosx
Principal Value of inverse functions
-90 o ≤ sin -1x ≤ 90 o
-90 o ≤ tan -1x ≤ 90 o0 o ≤ cos -1x ≤ 180 o
Range of values of cos and sin
-1 ≤ cos x ≤ 1-1 ≤ sin x ≤ 1
Angle in Radians and Degrees
1 radian = (π/ 180) o1o = (180/ π ) rad
Amplitude and period of graphs
For y = a cos(bx + c) + d or y = a sin (bx + c) + d
Period = 360 o/bAmplitude = |a|maximum value = |a| +dminimum value = – |a| + d
For y = a tan(bx+c)Period = 180 o/b
Graph of y = sin x
Graph of y = cos x
Graph of y = tan x
To solve trigonometry equations, you need to know when sin/ cos/ tan are positive (or negative). Remember this quadrant, or the A-S-T-C in short.
You use trigonometric identities for solving and proofing identity questions. These identities are inside your formula booklet, you don’t need to memorize them. Just know that they are there.
This is not in your formula booklet. Make sure you know them:
a sin x ± b cos x = R cos (x ± α) a cos x ± b sin x = R cos (x ∓ α)
R = square root(a2 + b2)α = tan-1 (b/a)
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