Cofunction identities

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Intros
Lessons
  1. What are cofunction identities?
    • Relationships between trigonometric functions and their cofunctions
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Examples
Lessons
  1. 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})
    1. Solve for xx
      1. sin(xπ4)=cos(π12+3x)\sin(x-\frac{\pi}{4})=\cos(\frac{\pi}{12}+3x)
      2. cot(8+x)=tan(4x3)\cot(8^{\circ}+x)=\tan(4x-3^{\circ})
      3. csc(3x+π5)=sec(2xπ10)\csc(3x+\frac{\pi}{5})=\sec(2x-\frac{\pi}{10})
    Topic Notes
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    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)