Cofunction identities

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  1. What are cofunction identities?
    • Relationships between trigonometric functions and their cofunctions
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Examples
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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⁡(x−π4)=cos⁡(π12+3x)\sin(x-\frac{\pi}{4})=\cos(\frac{\pi}{12}+3x)
      2. cot⁡(8∘+x)=tan⁡(4x−3∘)\cot(8^{\circ}+x)=\tan(4x-3^{\circ})
      3. csc⁡(3x+π5)=sec⁡(2x−π10)\csc(3x+\frac{\pi}{5})=\sec(2x-\frac{\pi}{10})
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    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⁡(π2−θ)=cos⁡(θ)\sin(\frac{\pi}{2}-\theta)=\cos(\theta)
    sin⁡(θ)=cos⁡(π2−θ)\sin(\theta)=\cos(\frac{\pi}{2}-\theta)
    tan⁡(π2−θ)=cot⁡(θ)\tan(\frac{\pi}{2}-\theta)=\cot(\theta)
    tan⁡(θ)=cot⁡(π2−θ)\tan(\theta)=\cot(\frac{\pi}{2}-\theta)
    sec⁡(π2−θ)=csc⁡(θ)\sec(\frac{\pi}{2}-\theta)=\csc(\theta)
    sec⁡(θ)=csc⁡(π2−θ)\sec(\theta)=\csc(\frac{\pi}{2}-\theta)
    Basic Concepts
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