Question Video: Using Periodic Identities to Find the Value of a Trigonometric Function Involving Special Angles Mathematics

Video Transcript

Find the value of the cos of 11𝜋 over six.

We begin by noticing that our angle is given in radians, and we recall that 𝜋 radians is equal to 180 degrees. Dividing both values by six, we see that 𝜋 over six radians is equal to 30 degrees. We can then multiply both sides of this equation by 11, showing us that 11𝜋 over six radians is equal to 330 degrees. This means that the value we need to calculate is the cos of 330 degrees. We can do this by firstly sketching the graph of the cosine function and then using our knowledge of special angles.

The cosine function is periodic and has a maximum value of one and a minimum value of negative one. The graph of 𝑦 equals cos of 𝜃 between zero and 360 degrees is shown. We want to calculate the cos of 330 degrees. From our graph, we can see that this is positive and lies between zero and one. Due to the symmetry of the cosine function, we can see from our graph that the cos of 330 degrees is equal to the cos of 30 degrees. One of the special angles we need to recall is that the cos of 30 degrees is equal to root three over two. This means that the cos of 330 degrees is also equal to root three over two. The cos of 11𝜋 over six radians is, therefore, also equal to root three over two.