Between 0^@0∘ and 90^@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")cosA=adjacent sidehypotenuse
To see the performance of the ratio as we increase the angle AA, keeping hypotenuse same, we know adjacent side continues to reduce and when AA becomes 90^@90∘, adjacent side reduces to 00. 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^@=1cos0∘=1, it continues ro reduce and at 90^@90∘, we have cos90^@=0cos90∘=0
Hence, cos35^@ < cos45^@cos35∘<cos45∘ is FALSE. Rather, we have cos35^@ > cos45^@cos35∘>cos45∘.
