[Hiralis]

Sup? Basically, I'm going to make a guide you can refer to for maths whenever you might need it, e.g. revision.

Trigonometry

So, basically, when it comes to trig, you always need to remember these basic things.

1. "Soh Cah Toa"
Soh - SinΘ(Theta) = Opp ÷ Hyp (Opposite divide hypotenuse)
Cah - CosΘ = Adj ÷ Hyp
Tan - TanΘ = Opp ÷ Adj

2. "If it's on top, multiply, if it's on the bottom, divide them"
This basically speaks for itself. If the "x" is on the top of the equation, you multiply it by the ratio (sin, cos, tan) and the angle.
e.g x = 34 x sin32
= 18.017....
~ 18
If the "x" is on the bottom of the equation, you divide it by the ratio and angle.
e.g x = 45 ÷ tan28
= 84.632....
~ 84.6

3. Power of Negative 1
To find the angle using any cos, tan, or sin ratio, you have to use the shift function and use "sin to power of -1" or cos, or tan.
e.g. Θ = sin-1 (34 ÷ 45)
= sin-1 (0.7555555...)
= 49.0739....
~ 49

Now, let's do these problems.


sinΘ = O ÷ H
sin30 = x ÷ 10
x = 10 x sin30
= 5


Now, you can choose any angle here, I'll be choosing the angle at "J"

cosΘ = A ÷ H
cosΘ = 4 ÷ 6
Θ = sin-1 (4 ÷ 6)
= 48.189....
~ 48.2


There's the lesson on trigonometry done for the day, enjoy, use it to revise if you like.