Cofunction identities

All in One Place

Everything you need for JC, LC, and college level maths and science classes.

Learn with Ease

We’ve mastered the national curriculum so that you can revise with confidence.

Instant Help

24/7 access to the best tips, walkthroughs, and practice exercises available.

0/1
?
Intros
Lessons
  1. What are cofunction identities?
    • Relationships between trigonometric functions and their cofunctions
0/4
?
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
    ?
    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)