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Give the exact value of: `cos((11pi)/4)` `sin((7pi)/6)` `tan((5pi)/3)`

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peuco7 | Student, Grade 10 | Honors

Posted March 25, 2012 at 9:11 PM via web

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Give the exact value of:

`cos((11pi)/4)`

`sin((7pi)/6)`

`tan((5pi)/3)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 25, 2012 at 9:28 PM (Answer #1)

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The exact value of  `cos((11pi)/4)` ,` sin((7pi)/6)` and `tan((5pi)/3) ` has to be determined.

`cos((11pi)/4)`

=> `cos (2*pi + pi - pi/4)`

=> `cos(pi - pi/4)`

=> `-cos(pi/4)`

=> `-1/sqrt 2`

`sin((7*pi)/6)`

=> `sin(pi + pi/6)`

=> `-sin(pi/6)`

=> -0.5

`tan((5*pi)/3)`

=> `tan(pi + (2*pi)/3)`

=> `tan((2*pi)/3)`

=> `-sqrt 3`

The required values are: `cos((11pi)/4) = -1/sqrt 2` , `sin((7pi)/6) = -0.5 ` and `tan((5pi)/3) = -sqrt 3`

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