Sine, cosine, tangent and their applications
In a right triangle, sin(θ) =
SOH-CAH-TOA: Sine = Opposite/Hypotenuse
If cos(θ) = 3/5, what is sin(θ)?
Use identity sin²θ + cos²θ = 1, so sinθ = √(1 - (3/5)²) = 4/5
Find tan(45°)
In 45-45-90 triangle, legs are equal, so opposite/adjacent = 1
A ladder leans against a wall. If angle with ground is 60° and ladder is 10m long, how high up the wall does it reach?
Height = ladder × sin(60°) = 10 × (√3/2) = 5√3
What is cos(90°)?
At 90°, adjacent side = 0, so cos(90°) = 0/hypotenuse = 0