Question

Which is larger \[\sin\ 24^{o}\] or \[\cos\ 24^{o}\] ?
A. \[\sin\ 24^{o}\]
B. \[\cos\ 24^{o}\]
C. Both are equal
D. Cannot be compared

Answer 1

Hint: In this question, we need to find which is larger one \[\sin\ 24^{o}\] or \[\cos\ 24^{o}\] . The symbol used for greater than is \[>\] and less than is \[<\]. Mathematically, equality and inequality symbols are used to compare the two given numbers.First, we need to split the angle \[24^{o}\]. Then by using the property \[\sin(90^{o} - \theta) = \cos\ \theta\] , we can rewrite the function in the form of a cosine function. Then we need to compare the two functions which are in the form of a cosine function to find which is larger one.

Complete step by step answer:
Given, \[\sin\ 24^{o}\] and \[\cos\ 24^{o}\].Here we need to find which function is larger one.First let us consider the function \[\sin\ 24^{o}\].Now we need to split the angle \[24^{o}\].By splitting the angle we get,
\[\sin\ 24 = \sin(90^{o} – 66^{o})\]
By using the property \[\sin(90^{o} - \theta) = \cos\ \theta\] we get,
\[\Rightarrow \ \cos\ 66^{o}\]

Now we can compare the two functions easily. On comparing \[\cos\ 66^{o}\] and \[\cos\ 24^{o}\].We can conclude that \[\cos\ 24^{o} > \cos\ 66^{o}\] . Since in the first quadrant, \[\cos\ \theta\] is increasing. Thus \[\cos\ 24^{o}\] is the larger one. Hence \[\cos\ 24^{o} > \sin\ 24^{o}\]

Therefore, option B is the correct answer.

Note: In order to solve these types of questions, we should have a strong grip over trigonometric functions and properties. Mathematically, while comparing two or more numbers or functions symbols play a major role. Symbols such as Less than symbol , greater than symbol, less than or equal to, greater than or equal to symbol and equal to symbol are used. We can also consider \[\cos\ 24^{o}\] and split it as \[\cos(90^{o} – 66^{o})\] which results as \[\sin\ 66^{o}\] . Then we can easily compare both the functions.