Determine whether the following statement is true or false. The cos of 25 degrees is less than the cos of 10 degrees.
We will answer this question using two methods. Firstly, we will just evaluate the expressions using a calculator, and secondly we will study the cosine graph. When inputting any trigonometric function into the calculator, it is important we’re in the correct mode. In this question, we need to be in degree mode. This is usually denoted by a capital D in the top right-hand corner of the screen.
To calculate the cos of 25 degrees, we begin by pressing the cosine button. We then input the argument 25 and finally close the parentheses. Pressing the equals button, we see that the cos of 25 degrees is equal to 0.9063 and so on. We can repeat this process to calculate the cos of 10 degrees. This is equal to 0.9848 and so on. 0.9063 is less than 0.9848. This means that the cos of 25 degrees is less than the cos of 10 degrees. And the statement in the question is therefore true.
An alternative method here would be to consider the graph of the cosine function. Our sketch shows the cosine function between zero and 180 degrees. We can see from this graph that cos 𝑥 is decreasing between zero and 180 degrees. This means that as our value of 𝑥, the angle or argument, increases, cos 𝑥 decreases. And since 25 degrees is greater than 10 degrees, then cos of 25 degrees will be less than cos of 10 degrees. This once again confirms that the statement is true.