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# what are the solutions in the interval: 0 <= θ <= 2pi

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8. Solve each of the following trigonometric equations and find all solutions in the interval

b. sin x + sqrt2 = -sin x

c. 3tan^2 x - 1 = 0

d. 2cos(3x - 1) = 0

f. 2sin^2 x - x - 1 = 0

Feb 23, 2019

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b)

$$sin x + \sqrt2 = -sin x\\ 2sinx=-\sqrt2\\ sinx=-\frac{\sqrt2}{2}\\ sinx=-\frac{1}{\sqrt2}\qquad \text{3rd and 4th quads}\\ x=180+45,\;\;\;or\;\;\;360-45\\ x=225^\circ\;\;\;or\;\;\;315^\circ\\$$

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Feb 23, 2019