How do you find the exact value of #arccos (-sqrt3/2)#?

Answer 1

The angle whose cosine is #(-sqrt3/2)# is 150 degrees or #5/6pi#

Draw an equilateral triangle. Cut it in half . The angles in this right angle triangle are 30 ,60, 90 If the hypotenuse is length 2 then the shortest side is 1 and from Pythagoras the other side is #sqrt3# So the angle whose cosine is #sqrt3/2# is 30 degrees. Now sketch the cosine graph. From this you can find the angle whose cosine is #(-sqrt3/2)# Is 150 degrees or #5/6pi#
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Answer 2

To find the exact value of ( \arccos\left(-\frac{\sqrt{3}}{2}\right) ), you use the unit circle. Since the cosine function represents the x-coordinate on the unit circle, you're looking for the angle whose cosine is ( -\frac{\sqrt{3}}{2} ).

The angle ( \arccos\left(-\frac{\sqrt{3}}{2}\right) ) corresponds to ( \frac{5\pi}{6} ) radians or ( 150^\circ ). Therefore, the exact value is ( \frac{5\pi}{6} ) radians or ( 150^\circ ).

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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.

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.

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.

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.

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