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Find the exact value of cos(13pi/12)

Find the exact value of
cos(13pi/12)

Grade:11

2 Answers

Ranganna palem Srikanth
35 Points
6 years ago
 Exact answer of cos (13pi/12) is -1.833...... because cos (pi) is always -1
 
Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

A = cos(\frac{13\pi }{12})
A = cos(\pi +\frac{\pi }{12})
A = -cos(\frac{\pi }{12})
cos(\frac{\pi }{6}) = 2cos^{2}(\frac{\pi }{12}) - 1
2cos^{2}(\frac{\pi }{12}) = 1 + cos(\frac{\pi }{6})
cos(\frac{\pi }{12}) = \sqrt{\frac{1 + cos(\frac{\pi }{6})}{2}}
cos(\frac{\pi }{12}) = \sqrt{\frac{1 + \frac{\sqrt{3} }{2}}{2}}
cos(\frac{\pi }{12}) = \sqrt{\frac{2 + \sqrt{3}}{4}}
A = - cos(\frac{\pi }{12}) = -\sqrt{\frac{2 + \sqrt{3}}{4}}

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