Example: Graph of cosine | Graphs of trig functions | Trigonometry | Khan Academy

TL;DR

The video explains the graph of y = cosine theta and determines the values of theta for which cosine theta equals one and negative one.

Transcript

• [Instructor] In the graph below, for what values of theta does cosine of theta equal one, and for what values of theta does cosine of theta equal negative one? And they've very nicely graphed it for us, the horizontal axis is the theta axis, and the vertical axis is the y-axis, and so this is the graph of y is equal to cosine of theta. And it mak... Read More

Key Insights

• 📈 The graph represents the values of cosine theta for different angles.
• 🤨 Cosine theta equals one when theta is a multiple of two pi and negative one when theta is an odd multiple of pi.
• 🤨 The graph repeats itself every two pi in both directions.
• 👈 The x-coordinate of points on the unit circle corresponds to the value of cosine theta.

Questions & Answers

Q: What does the graph of y = cosine theta represent?

The graph represents the values of cosine theta for different angles, with theta on the x-axis and y = cosine theta on the y-axis.

Q: When does cosine theta equal one?

Cosine theta equals one when theta is equal to any multiple of two pi, such as zero, two pi, four pi, etc. It repeats every two pi.

Q: When does cosine theta equal negative one?

Cosine theta equals negative one when theta is equal to any odd multiple of pi, such as pi, three pi, five pi, etc. It also repeats every two pi in the negative direction.

Q: How can we determine the values of theta for which cosine theta equals one and negative one?

By analyzing the graph, we can observe the points where y = cosine theta is equal to one and negative one, which occur at specific intervals of two pi for one, and two pi with an offset of pi for negative one.

Summary & Key Takeaways

• The graph of y = cosine theta represents the values of cosine of theta for different theta angles.

• When theta is equal to zero or any multiple of two pi, cosine theta equals one.

• When theta is equal to pi or any odd multiple of pi, cosine theta equals negative one.