Value of cos 106° is:
(1) \(\frac{7}{25}\)
(2) \(-\frac{7}{25}\)
(3) \(\frac{24}{25}\)
(4) \(-\frac{24}{25}\)
Answer (2)
To find the value of cos 10 6 ∘ , we need to understand the properties of the cosine function.
Cosine is an even function and it's periodic, which means it repeats its values every 360 degrees. The cosine function is defined for any angle, and its value can be found using a calculator or through trigonometric identities and tables.
The angle 10 6 ∘ is located in the second quadrant of the unit circle. In the second quadrant, the cosine function is negative. Thus, any positive angle between 9 0 ∘ and 18 0 ∘ will have a negative cosine value.
To approximate cos 10 6 ∘ without a calculator, you could use a cosine table or calculator to find its exact value:
cos 10 6 ∘ ≈ − 0.2419
Looking at the options given:
25 7 ≈ 0.28
− 25 7 ≈ − 0.28
25 24 = 0.96
− 25 24 = − 0.96
Since cos 10 6 ∘ ≈ − 0.2419 is closest to option 2,
− 25 7 ≈ − 0.28 ,
The correct answer is (2) − 25 7 .
The value of cos 10 6 ∘ is negative, as it lies in the second quadrant. The closest approximation from the given options is (2) − 25 7 . Therefore, the correct choice is (2).
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