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Answer 1 · 2016-10-16T00:44:57

Here's a few examples of the trigonometric equations you may be required to solve.

Solve the equation $4 {sin}^{2} x = 1$ $4sin^2x = 1$

Isolate $x$ $x$ .

${sin}^{2} x = \frac{1}{4}$ $sin^2x = 1/4$

$sin x = \pm \frac{1}{2}$ $sinx = +-1/2$

$x = arcsin (\pm \frac{1}{2})$ $x = arcsin(+-1/2)$

$x = 30˚, 150˚, 210˚, 330˚$

Solve the equation $cos^2x = 2sin^2x + 2sinx$

Apply the identity $cos^2x + sin^2x = 1 -> cos^2x = 1 - sin^2x$

$1 - sin^2x = 2sin^2x + 2sinx$

$0 = 3sin^2x + 2sinx - 1$

$0 = 3sin^2x + 3sinx - sinx - 1$

$0 = 3sinx(sinx + 1) - 1(sinx + 1)$

$0 = (3sinx - 1)(sinx + 1)$

$sinx = 1/3 and sinx = -1$

$x = arcsin(1/3) and 270˚$

Solve the equation $cscx xx tanx = cotx xxsinx$

Apply the following identities:

• $cscx = 1/sinx$
• $tanx = sinx/cosx$
• $cotx = cosx/sinx$

$1/sinx xx sinx/cosx = cosx/sinx xx sinx$

$1/cosx = cosx$

$1 = cos^2x$

$0 = cos^2x - 1$

$0 = (cosx + 1)(cosx - 1)$

$cosx = -1 and cosx = 1$

$x = 0˚ and 180˚$

However, these solutions are extraneous, since they render the original equation undefined with cotangent.

Solve the equation $sin(45˚ + x) = 1$

$45˚ + x = arcsin1$

$x = 90˚ - 45˚$

$x = 45˚$

The key to solving trigonometric equations is knowing your identities.

Hopefully this helps!