What is the cosine of 135 degrees?
Answer (3)
cos 13 5 o = cos ( 9 0 o + 4 5 o ) = − s in 4 5 o = − 2 2 re d u c t i o n f or m u l a s : cos ( 9 0 o + α ) = − s in α
cos ( 18 0 0 − α ) = − cos α cos 13 5 0 = cos ( 18 0 0 − 4 5 0 ) = − cos 4 5 0 = − 2 2
The cosine of 135 degrees is found by using its reference angle of 45 degrees, which has a cosine of 2 2 . Since 135 degrees lies in the second quadrant, the cosine value is negative, resulting in − 2 2 . Thus, cos ( 13 5 ∘ ) = − 2 2 .
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