# trig

Solve the triginometric equation analytically. Use values of x for 0 less then or equal to x less then 2pi

The equation for this question is sin2x + cos2x = 0

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sin2x = -cos2x, now divide by cos2x
sin2x/cos2x = -1
tan2x = -1
so 2x = 135 or 315º
so x = 67.5 or x = 157.5º

now remember that the period of tan(kß) is 180/k

so the period of tan2x is 90º, which means that if we add 90º to any of our answers we get a new answer as long as we are in our given domain.

so x = 67.5, 157.5, 247.5, 337.5

again, it would be a good idea to check these with your calculator.

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