Cofunction identities

Cofunction identities

Lessons

Cofunction Identities: Basically, we need the sum of the left and right brackets to be 90° or π2\frac{\pi}{2}

sin(π2θ)=cos(θ)\sin(\frac{\pi}{2}-\theta)=\cos(\theta)
sin(θ)=cos(π2θ)\sin(\theta)=\cos(\frac{\pi}{2}-\theta)
tan(π2θ)=cot(θ)\tan(\frac{\pi}{2}-\theta)=\cot(\theta)
tan(θ)=cot(π2θ)\tan(\theta)=\cot(\frac{\pi}{2}-\theta)
sec(π2θ)=csc(θ)\sec(\frac{\pi}{2}-\theta)=\csc(\theta)
sec(θ)=csc(π2θ)\sec(\theta)=\csc(\frac{\pi}{2}-\theta)
  • 1.
    What are cofunction identities?
    • Relationships between trigonometric functions and their cofunctions

  • 2.
    Write the following in terms of its cofunction:

    \blacksquare sin(23)\sin(23)
    \blacksquare cos(47)\cos(47)
    \blacksquare tan(π6)\tan(\frac{\pi}{6})
    \blacksquare csc(π6)\csc(\frac{\pi}{6})

  • 3.
    Solve for xx
    a)
    sin(xπ4)=cos(π12+3x)\sin(x-\frac{\pi}{4})=\cos(\frac{\pi}{12}+3x)

    b)
    cot(8+x)=tan(4x3)\cot(8^{\circ}+x)=\tan(4x-3^{\circ})

    c)
    csc(3x+π5)=sec(2xπ10)\csc(3x+\frac{\pi}{5})=\sec(2x-\frac{\pi}{10})