Part of trigonometry that studies the properties of circular functions of angles and arcs.
Properties
The Pythagorean identities are:
- cos\(^{2}\)(θ) + sin\(^{2}\)(θ) = 1
- 1 + tan\(^{2}\)(θ) = sec\(^{2}\)(θ)
- 1 + cot\(^{2}\)(θ) = cosec\(^{2}\)(θ)
The formulas for the sum and difference of two angles are:
- cos(θ + φ) = cos(θ) cos(φ) – sin(θ) sin(φ)
- cos(θ – φ) = cos(θ) cos(φ) + sin(θ) sin(φ)
- sin(θ + φ) = sin(θ) cos(φ) + sin(φ) cos(θ)
- sin(θ – φ) = sin(θ) cos(φ) – sin(φ) cos(θ)
- tan(θ + φ) = \(\dfrac{\textrm{tan}(\textit{θ}) + \textrm{tan}(\textit{φ})}{1 -\textrm{tan}(\textit{θ})\textrm{tan}(\textit{φ})}\)
- tan(θ – φ) =\(\dfrac{\textrm{tan}(\textit{θ}) − \textrm{tan}(\textit{φ})}{1 +\textrm{tan}(\textit{θ})\textrm{tan}(\textit{φ})}\)