How do you find the solution to #2costheta-1=0# if #0<=theta<360#?

Answer 1

Samantha Abate

#S={60^@,300^@}#

#2 cos theta-1=0#

#2cos theta = 1#

#cos theta = 1/2#

#theta = cos^-1 (1/2)#

#theta=+- 60^@ + 360^@ n#, where n are integers

#n=0, theta = 60^@, -60^@#

#n=1, theta = 420^@, 300^@#

#S={60^@,300^@}#

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Answer 2

Brooklyn Anderson

To find the solution to (2\cos(\theta) - 1 = 0) for (0 \leq \theta < 360^\circ), follow these steps:

Add 1 to both sides of the equation: [2\cos(\theta) = 1]
Divide both sides by 2: [\cos(\theta) = \frac{1}{2}]
Find the angles where (\cos(\theta) = \frac{1}{2}) within the given range of (0 \leq \theta < 360^\circ). These angles are 60° and 300°.

So, the solutions are: [\theta = 60^\circ \text{ and } \theta = 300^\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.

How do you find the solution to #2costheta-1=0# if #0&lt;=theta&lt;360#?

How do you find the solution to #2costheta-1=0# if #0<=theta<360#?