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:
- c
^{2}= a^{2}+ b^{2 }– 2abcos∠C

- c

## Trigonometric Ratios

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* = sin*x* / cos*x*

# Principal Value of inverse functions

-90 ^{o} ≤ sin ^{-1}*x* ≤ 90 ^{o}

-90 ^{o} ≤ tan ^{-1}*x* ≤ 90 ^{o}0 ^{o} ≤ cos ^{-1}*x *≤ 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) ^{o}1^{o} = (180/ π ) rad

## Amplitude and period of graphs

For *y* = a cos(b*x* + c) + d or *y* = a sin (b*x* + c) + d

Period = 360 ^{o}/bAmplitude = |a|maximum value = |a| +dminimum value = – |a| + d

For *y* = a tan(b*x*+c)Period = 180 ^{o}/b

## Graph of y = sin *x*

## Graph of y = cos *x*

## Graph of y = tan *x*

## 4 Quadrants

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.

## Trigonometric Identities

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.

## R- Formula

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(a^{2} + b^{2})α = tan^{-1} (b/a)

## Want to learn more about Trigonometry for O Level Add Maths?

Trigonometry is a big topic in O Level Additional Mathematics. From the notes above, you can see the many different concepts tested. For the O Level exam, there are usually a few questions on trigonometry testing various different concepts. This is a chapter that many students struggle because there’s just so many things to know.

In my course on Trigonometry, I go into detail not only the concepts but how to apply them in different scenarios. We will go through many exam questions together step-by-step so that students finish the course equipped with the skills needed to tackle their test and exam questions on trigonometry with confidence. You can purchase the course instantly on Udemy, and watch and learn instantly. Get the course on Trigonometry here.