Question Video: Graphs of Trigonometric Functions | Nagwa Question Video: Graphs of Trigonometric Functions | Nagwa

Question Video: Graphs of Trigonometric Functions Mathematics • First Year of Secondary School

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Which of the following is the graph of 𝑦 = cos 𝑥? [A] Graph (A) [B] Graph (A) [B] Graph (C) [D] Graph (D) [E] Graph (E)

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Video Transcript

Which of the following is the graph of 𝑦 equals cos of 𝑥?

Remember, one of the key features of the cosine graph is that it has a 𝑦-intercept of one. This means we can immediately disregard any graphs that don’t pass through the point zero, one. So, we can get rid of options (B), (D), and (E) straightaway. Next, we know that it’s a periodic function and that it repeats every 360 degrees. Option (C) appears to have a much smaller period; in fact, it repeats every 120 degrees, so it can’t be this one.

This leaves only option (A). Let’s check by looking at the other properties. Some of the roots of 𝑦 equals cos of 𝑥 are 90 degrees, 270 degrees, and negative 90 degrees. We can see that option (A) passes through all of these values on the 𝑥-axis. The curve has maxima at one and minima at negative one. It is also an even function, so it’s symmetric over the 𝑦-axis. Hence, we have confirmed that option (A) is indeed the graph of 𝑦 equals cos of 𝑥.

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