What is the number of degrees in the measure of angle #x# that satisfies the equation #2cos(x) - 1 =0# in the interval #180°<=x<=360°#?

Answer 1

#300^@#

2cos x - 1 = 0 #cos x = 1/2# Trig table and unit circle --> #cos x = 1/2# --> arc # x = +- 60^@# In the interval (180 < x < 360, there is one answer: #x = - 60^@,# or #x = 300^@# (co-terminal)

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Answer 2

Aaliyah Abdullah

To find the measure of angle ( x ) that satisfies the equation ( 2\cos(x) - 1 = 0 ) in the interval ( 180^\circ \leq x \leq 360^\circ ), we need to solve for ( x ).

Given ( 2\cos(x) - 1 = 0 ), [ 2\cos(x) = 1 ] [ \cos(x) = \frac{1}{2} ]

In the interval ( 180^\circ \leq x \leq 360^\circ ), the cosine function is positive in the second and third quadrants. In these quadrants, the cosine function takes on the value ( \frac{1}{2} ) at ( 60^\circ ) and ( 300^\circ ).

Therefore, the solutions for ( x ) in the given interval are ( x = 120^\circ ) and ( x = 240^\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.

What is the number of degrees in the measure of angle #x# that satisfies the equation #2cos(x) - 1 =0# in the interval #180°&lt;=x&lt;=360°#?

What is the number of degrees in the measure of angle #x# that satisfies the equation #2cos(x) - 1 =0# in the interval #180°<=x<=360°#?