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**AlphaRock** **#1** Solve: sqrt(3)(cos(x)tan(x) + cos(x) = 0, where 0 <= x <= 2pi

My work:

cos(x)[sqrt(3)tan(x) + 1] = 0

cos(x) = 0

x = pi/2, 3pi/2

sqrt(3)tan(x) + 1 = 0

tan(x) = -1/(sqrt(3)) = opp/adj

x = 60

**Answer:**5pi/6, 11pi/6

**#2** Solve: cos(2x) - 3sin(x) = 2, where -pi <= x <= pi

1 - (sin(x))^2 - 3sin(x) = 2

-1 - (sin(x))^2 - 3sin(x) = 0

Unsure how to continue...

**Answer: **4pi/3, 5pi/3, 3pi/2

**#3** Solve: 2cos(x) = 2^x

Work: Tried to graph it, but didn't really work out.

Answer: -1.38, 0 , 0.66