SOLUTION: find the value of cos 105 degrees without using a calculator.retain radical notation.
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Question 231699: find the value of cos 105 degrees without using a calculator.retain radical notation.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \cos{\alpha}\cos{\beta}\ -\ \sin{\alpha}\sin{\beta})
}\ =\ \frac{\sqrt{2}}{2})
}\ =\ \frac{1}{2})
}\ =\ \frac{\sqrt{2}}{2})
}\ =\ \frac{\sqrt{3}}{2})
}\ =\ \cos{(45)}\cos{(60)}\ -\ \sin{(45)}\sin{(60)})
}\ =\ \left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2}\right)\ -\ \left(\frac{\sqrt{2}}{2}\right)\left(\frac{\sqrt{3}}{2}\right))
Simplification of this expression is left as an exercise for the student.
Sanity check: Notice that the left hand term is smaller than the right hand term. That means that cos(105) < 0, which makes sense for a Quadrant II angle.
John
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