Explanation
In trigonometry, we often use the values of:
- Sine (sin)
- Cosine (cos)
- Tangent (tan)
for the angles:
👉 0°, 30°, 45°, 60°, and 90°
Instead of memorizing them, we can use a simple trick to find them quickly.
Formula / Rule
Step 1 – Sine values (sin)
Write:
√(0/4), √(1/4), √(2/4), √(3/4), √(4/4)
So:
sin(0°) = 0
sin(30°) = 1/2
sin(45°) = 1/√2
sin(60°) = √3/2
sin(90°) = 1
Step 2 – Cosine values (cos)
👉 Reverse the sine values:
cos(0°) = 1
cos(30°) = √3/2
cos(45°) = 1/√2
cos(60°) = 1/2
cos(90°) = 0
Step 3 – Tangent values (tan)
Use:
tan(θ) = sin(θ) / cos(θ)
Example
Find tan(60°).
Step 1:
tan(θ) = sin(θ) / cos(θ)
Step 2:
tan(60°) = (√3/2) ÷ (1/2)
Step 3:
Multiply by reciprocal
= (√3/2) × (2/1)
Step 4:
= √3
👉 Final Answer:
tan(60°) = √3