On the trig unit circle,
cos(5π/6)=cos(−π/6+π)=−cos(π/6)
Trig Table of Special Arcs gives
cos(5π/6)=−cos(π/6)=-[tex] \frac{ \sqrt{3} }{2} [/tex]
The exact value of cos 5pi/6 would be [tex]\dfrac{\sqrt{3} }{2}[/tex].
Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
To find the equivalent in the first quadrant to an angle in the fourth quadrant, then:
[tex]cos\dfrac{ 5\pi }{6} =cos \dfrac{-\pi}{6+\pi } \\\\=-cos\dfrac{ \pi }{6}[/tex]
applying the equivalent angle:
[tex]cos\dfrac{ 5\pi }{6} =-cos\dfrac{ \pi }{6}\\\\= \dfrac{\sqrt{3} }{2}[/tex]
Therefore, the exact value of cos 5pi/6 would be [tex]\dfrac{\sqrt{3} }{2}[/tex].
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