How do you solve #cos(2t)=1/2#?
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To solve the equation ( \cos(2t) = \frac{1}{2} ), you can use the inverse cosine function (also known as arccosine or cos^(1)). Here are the steps:

Take the inverse cosine of both sides of the equation: [ 2t = \cos^{1}\left(\frac{1}{2}\right) ]

Determine the values of ( \cos^{1}\left(\frac{1}{2}\right) ). This value corresponds to angles whose cosine is ( \frac{1}{2} ). The common angles with cosine ( \frac{1}{2} ) are ( \frac{\pi}{3} ) and ( \frac{5\pi}{3} ).

Since the cosine function has a period of ( 2\pi ), you can add multiples of ( 2\pi ) to the angles found in step 2. So, the general solution for ( 2t ) is: [ 2t = \frac{\pi}{3} + 2\pi n \quad \text{and} \quad 2t = \frac{5\pi}{3} + 2\pi n ] where ( n ) is an integer.

Finally, solve for ( t ) by dividing both sides by 2: [ t = \frac{\pi}{6} + \pi n \quad \text{and} \quad t = \frac{5\pi}{6} + \pi n ] where ( n ) is an integer.
These are the solutions for ( t ) that satisfy the equation ( \cos(2t) = \frac{1}{2} ).
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When evaluating a onesided 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 onesided 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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