How do you determine if #cos35^circ<cos45^circ# is true or false?

1 Answer
Mar 17, 2017

Answer:

#cos35^@ < cos45^@# is FALSE

Explanation:

Between #0^@# and #90^@#, the cosine function is a decreasing function. For this let us start from the definition of cosine function. As we know, in a right angled triangle, such as one given below:
enter image source here
#cosA=("adjacent side")/("hypotenuse")#

To see the performance of the ratio as we increase the angle #A#, keeping hypotenuse same, we know adjacent side continues to reduce and when #A# becomes #90^@#, adjacent side reduces to #0#. This is also seen from its graph too
graph{cos((pix)/180) [-7.03, 153, -0.5, 1.5]}

and we observe that while #cos0^@=1#, it continues ro reduce and at #90^@#, we have #cos90^@=0#

Hence, #cos35^@ < cos45^@# is FALSE. Rather, we have #cos35^@ > cos45^@#.