𝗔𝗖𝖳 𝗆𝗮𝘁𝗁 𝗆𝘂𝘀𝗍-𝗄𝗻𝗈𝘄𝘀 (𝘁𝗋𝗂𝗴 𝖾𝗱𝗂𝗍𝗶𝗼𝗇) ୨୧

Studying trig? Don’t be sin-ical, it’s all about the right angle! haha so funny am I right guys

What is SOH-CAH-TOA?

• SOH- opposite/hypotenuse

• CAH-adjacent/ hypotenuse

• TOA-opposite/ adjacent

Lowkey sounds like “suck my toe”. Now you will never forget it unfortunately. Sorry not sorry

Common angles (degrees/radians) on the unit circle

• 0° = 0

• 30° = π/6

• 45° = π/4

• 60° = π/3

• 90° = π/2

Radians vs. Degrees conversion

• Degrees → Radians: Multiply by π/180

• Radians → Degrees: Multiply by 180/π

Eg: convert to radians: 40degrees

40*180/π

=40π /180

=2π /9

Basic Pythagorean identities

• sin²θ + cos²θ = 1 (most important)

• 1 + tan²θ = sec²θ

• 1 + cot²θ = csc²θ

Reciprocal trig identities

• sinθ = 1/cscθ

• cosθ = 1/secθ

• tanθ = 1/cotθ

• cscθ = 1/sinθ

• secθ = 1/cosθ

• cotθ = 1/tanθ

How to remember the reciprocal trig identities?

SOH CAH TOA

CSC SEC COT

How I remember is: sec is like “second”, so it goes with cosine in soh cah toa. Cotangent is related to tangent, and the other one is kind of self explanatory

Side ratios of special triangles (30-60-90, 45-45-90)

• 30-60-90: 1 : √3 : 2 (short leg : long leg : hypotenuse)

• 45-45-90: 1 : 1 : √2 (leg : leg : hypotenuse)

Pro tip: In a 30-60-90 triangle, the short leg is always half the hypotenuse!

Common trig applications

• Angles of Elevation & Depression: Use tan(θ) = opposite/adjacent for height or distance problems.

• Ferris Wheel Problems:Think of sin(θ) and cos(θ) for circular motion and height changes.

• Harmonic Motion: When an object moves back and forth, it often follow motions like y = A\sin(Bx) or y=A/cos(Bx)

The last one is in more advanced trig problems( ˙꒳​˙ )

Another pro tip: If it involves height, shadows, or circular motion, it’s probably a trig problem!