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Solve #cosx=sqrt3/2# where #0lexle2pi#? How many solutions are possible? In which quadrants would you find the solutions? Determine the related angle to the equation? Determine all the solutions for the equation?

Answer 1

See below

Using the unit circle, determine how many times, the x-coordinate is equal to #sqrt3/2# in a complete period of #2pi# radians

Two solutions
Quadrant 1 and 4
#30°# or #pi/6# radians
#x=pi/6, (11pi)/6#
General solution:
#x= pi/6 +2pin#
# x= (11pi)/6+ 2pin#
Where n is an element of all integers

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Answer 2

Kai Anderson

The equation $\cos(x) = \frac{\sqrt{3}}{2}$ has two solutions in the interval $0 \leq x \leq 2\pi$ . The solutions are $x = \frac{\pi}{6}$ and $x = \frac{11\pi}{6}$ . These solutions are found in the first and fourth quadrants. The related acute angle to the equation is $\frac{\pi}{6}$ .

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.