# 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: $solve(\sin(x) = 0.5, x)$

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: $solve(\sin(x) = 0.5, x) \; | \; 0 \leq x \leq 4p$

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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