01.7-trigeqnscalc

Trigonometric Equations on the Classpad

General Solutions on the Classpad

  • Your classpad automatically gives a general solution to trig equations.
  • It uses constn(1) in place of n.
  • if more than one constant is required in a solution, it will use constn(2), constn(3) etc
  • Solve is available in the Keyboard. It is also available in the ACTION menu, ADVANCED submenu.

Example 1

… … Use the classpad to find the general solution in radians to $\sin(\theta) = \dfrac{1}{2}$

Solution:

  • Make sure the calculator is set to Standard and Radians

On the Main screen, enter: $solve(\sin(x) = 0.5, x)$

01.7calc1.JPG

The solutions should appear as: $\left\{ x=2 \cdot \pi \cdot constn(1) + \dfrac{\pi}{6},\, x=2 \cdot \pi \cdot constn(2) + \dfrac{5\pi}{6} \right\}$

Hence the solution is: $x = 2\pi n+ \dfrac{\pi}{6}, \; 2\pi n + \dfrac{5\pi}{6}, \quad n \in Z$

Note:

  • When writing the solutions,
  • you should write n and not constn(1).
  • you should NOT write the dot within each term
  • Don't forget to add $n \in J \; (\text{or } n \in Z )$ at the end.

Specified Domains on the Classpad

To specify a domain for the solution, after solve( …) type the symbol "|"

  • the "|" symbol is in the virtual keyboard, Math3 tab

Then type the domain in the format a < x < b

  • the "<" symbol is also in the virtual keboard,Math3 tab, (see below)
    • DON'T use the angle symbol

Example 2

… … Use the classpad to solve $\sin(\theta) = \dfrac{1}{2} \text{ in the domain } \theta \in [0, 4\pi]$

Solution:

  • Make sure the calculator is set to Standard and Radians

On the Main screen, enter: $solve(\sin(x) = 0.5, x) \; | \; 0 \leq x \leq 4p$

01.7calc2.jpg

The solution is: $x=\dfrac{\pi}{6},\, x=\dfrac{5 \pi}{6},\, x=\dfrac{13 \pi}{6},\, x=\dfrac{17 \pi}{6}$

  • Don't write calculator notation in your answer (so leave out the dots).

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