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

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.