How to evaluate sec 110^@?

Zion Robles

Zion Robles

Answered question

2023-03-15

How to evaluate sec 110 ° ?

Answer & Explanation

progutannx7f

progutannx7f

Beginner2023-03-16Added 7 answers

We given explanation: sec 110 = 1 cos 110 . Find cos 110 without using calculator.
Call cos (110) = cos x
Use this equation: cos 3 x = 4 cos 3 x - 3 cos x . We get:
cos 330 = cos (-30 + 360) = cos 30 = sqrt3/2
cos 330 = 3 2 = 4 cos 3 x - 3 cos x
4 cos 3 x - 3 cos x - 3 2 = 0
Use a graphing calculator to solve this cubic problem.
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
Hence:
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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