Trigonometry

Cards (10)

  • Radians to degrees conversion:
    2π=2\pi= 360
    π=\pi= 180
    π2\frac{\pi}{2} = 90
    π3=\frac{\pi}{3}= 60
    π4=\frac{\pi}{4}= 45
    π6=\frac{\pi}{6}= 30
  • Small angle approximations
    sinθ\sin\theta\approx θ\theta
    cosθ\cos\theta\approx 1θ221-\frac{\theta^2}{2}
    tanθ\tan\theta\approx θ\theta
  • Exact sine trig values
    sin30=\sin30= 12\frac{1}{2}
    sin60=\sin60= 32\frac{\sqrt{3}}{2}
    sin45=\sin45= 12\frac{1}{\sqrt{2}}
  • Tangent defnition
    tanθ=\tan\theta= sinθcosθ\frac{\sin\theta}{\cos\theta}
  • Solving equations
    sinθ=\sin\theta= sin(180θ)\sin\left(180-\theta\right) ±360°\pm360\degree
    cosθ=\cos\theta= cos(360θ)\cos\left(360-\theta\right) ±360°\pm360\degree
    tanθ=\tan\theta= tan(180+θ )\tan\left(180+\theta\ \right) ±180°\pm180\degree
  • Reciprocal trig functions
    cosecθ=\operatorname{cosec}\theta= 1sinθ\frac{1}{\sin\theta}
    secθ=\sec\theta= 1cosθ\frac{1}{\cos\theta}
    cotθ=\cot\theta= 1tanθ\frac{1}{\tan\theta}
  • Co-functions
    sinθ=\sin\theta= cos(90θ)\cos\left(90-\theta\right)
    cosθ=\cos\theta= sin(90θ)\sin\left(90-\theta\right)
  • Pythagorean identities
    sin2θ+\sin^2\theta+cos2θ=\cos^2\theta= 11
    1+1+tan2θ=\tan^2\theta= sec2θ\sec^2\theta
    1+1+cot2θ=\cot^2\theta= cosec2θ\operatorname{cosec}^2\theta
  • Double angle formulae
    sin2θ=\sin2\theta= 2sinθcosθ2\sin\theta\cos\theta
    cos2θ=\cos2\theta= cos2θsin2θ\cos^2\theta-\sin^2\theta
    cos2θ=\cos2\theta= 2cos2θ12\cos^2\theta-1
    cos2θ=\cos2\theta= 12sin2θ1-2\sin^2\theta
    tan2θ=\tan2\theta= 2tanθ1tan2θ\frac{2\tan\theta}{1-\tan^2\theta}
  • Addition formulae
    sin(A±B)=\sin\left(A\pm B\right)= sinAcosB±cosAsinB\sin A\cos B\pm\cos A\sin B
    cos(A±B)=\cos\left(A\pm B\right)= cosAcosBsinAsinB\cos A\cos B\mp\sin A\sin B
    tan(A±B)=\tan\left(A\pm B\right)= tanA±tanB1tanAtanB\frac{\tan A\pm\tan B}{1\mp\tan A\tan B}