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How do you evaluate #sec110°#?

Answer 1

Find #sec 110#

Ans: -2.94

#sec 110 = 1/(cos 110)#. Find cos 110 without using calculator. Call cos (110) = cos x Use the formula: #cos 3x = 4cos^3 x - 3cos x.# We get: cos 330 = cos (-30 + 360) = cos 30 = sqrt3/2 #cos 330 = sqrt3/2 = 4cos^3 x - 3cos x # #4cos^3 x - 3cos x - sqrt3/2 = 0# Solve this cubic equation by graphing calculator By estimation, we get; cos x = - 0.34 --> x = 110 (accepted) --> 3x = 330 cos x = - 0.65 --> x = 130 (rejected) --> 3x = 390 cos x = 0.98 --> x = 10 (rejected) --> 3x = 30 Finally: #sec (110) = 1/(-0.34) = - 2.94# graph{4x^3 - 3x - sqrt3/2 [-2.5, 2.5, -1.25, 1.25]}

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Answer 2

Elijah Alexander

To evaluate ( \sec(110^\circ) ), you first need to understand that ( \sec(\theta) ) represents the secant function, which is the reciprocal of the cosine function. Then, you evaluate ( \cos(110^\circ) ) and take its reciprocal to find ( \sec(110^\circ) ). So, ( \sec(110^\circ) ) is equal to ( \frac{1}{\cos(110^\circ)} ). After finding the cosine of ( 110^\circ ), you take its reciprocal to obtain the final answer.

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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.