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How to expand and collect trig identities on a TI-89 Titanium

By E-Code · updated

Press F2 9 (Trig) and 1 for tExpand(: tExpand(cos(x-y)) gives cos(x)·cos(y)+sin(x)·sin(y). F2 9 2 gives tCollect(, the opposite: tCollect((cos(x))^2) gives (cos(2·x)+1)/2.

Step by step

  1. Open Algebra, Trig. F2 9 Press F2 for Algebra, then 9 for Trig.
  2. Pick tExpand(. 1 Press 1 for tExpand(. It breaks up angle sums and multiple angles.
  3. Type cos(x-y). 2nd Z X − Y ) ) Press 2nd Z for cos( (COS is above Z), then type x-y and two ).
  4. Expand it. ENTER Press ENTER. You get the difference formula for cosine.
  5. Pick tCollect(. F2 9 2 Press F2, 9, then 2 for tCollect(. It does the opposite: powers and products become multiple angles.
  6. Type (cos(x))^2. ( 2nd Z X ) ) ^ 2 ) Type (, 2nd Z for cos(, x, two ), then ^2 and ).
  7. Collect it. ENTER Press ENTER.
  8. Read the identities. cos(x-y) = cos(x)cos(y)+sin(x)sin(y), and cos²(x) = (cos(2x)+1)/2: the power-reducing formula.

What the screen shows

cos(x-y) = cos(x)cos(y)+sin(x)sin(y), and cos²(x) = (cos(2x)+1)/2: the power-reducing formula.

Look for (cos(2·x)+1)/2 on the screen.

Try it with the keys lit up

This guide is one of E-Code's Learn lessons. Open it on E-Code's TI-89 calculator and each key lights up in turn as you press it.

Try “Expand and collect trig identities” on the TI-89 calculator

Related

Math programs for the TI-89 Titanium:

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