Trigonometry

Trigonometric Ratios

For a right Triangle with an acute Angle θ:

• sin θ = opposite / hypotenuse
• cos θ = adjacent / hypotenuse
• tan θ = opposite / adjacent

Memory aid: SOH-CAH-TOA

Finding a Side

If you know an Angle and one side, use the appropriate trig ratio to find unknown sides.

Example: In a right Triangle with Angle 35° and hypotenuse 10:

• Opposite = 10 × sin 35° ≈ 5.74
• Adjacent = 10 × cos 35° ≈ 8.19

Finding an Angle

Use inverse trig functions: θ = sin⁻¹(opp/hyp), θ = cos⁻¹(adj/hyp), θ = tan⁻¹(opp/adj).