Solution set to sin equation | Trigonometry | Khan Academy

TL;DR

The video explains how to find the solution set for the equation sine of X = 1/3 using the unit circle and inverse sine function.

Transcript

Voiceover:Which of these are contained in the solution set to sine of X is equal to 1/3? Answers should be rounded to the nearest hundredths. Select all that apply. I encourage you to pause the video right now and work on it on your own. I'm assuming you've given a go at it. Let's think about what this is asking. They're asking what are the X value... Read More

Key Insights

• 🥡 The solution set for sine of X = 1/3 includes two X values obtained by taking the inverse sine of 1/3 and subtracting or adding pi to it.
• 👨‍💼 The unit circle helps visualize the angles where the sine function equals 1/3.
• ☺️ Adding any multiple of two pi to the initial solution set values allows for more X values to be included.

Questions & Answers

Q: How can the solution set for sine of X = 1/3 be found?

The solution set can be found by taking the inverse sine of 1/3, subtracting or adding pi to it, and adding any multiple of two pi to those values.

Q: What is the role of the unit circle in finding the solution set?

The unit circle helps visualize the angles at which the sine function equals 1/3. By identifying these angles on the unit circle, the solution set can be determined.

Q: Can any multiple of two pi be added to the solution set values?

Yes, to obtain more X values where the sine of X is equal to 1/3, any multiple of two pi can be added to the initial solution set values.

Q: Are there any other values in the solution set?

No, only the X values obtained by taking the inverse sine of 1/3, subtracting or adding pi to it, and adding any multiple of two pi to those values are included in the solution set.

Summary & Key Takeaways

• The video discusses finding the solution set for sine of X = 1/3 using the unit circle.

• By visualizing the unit circle, it can be determined that there are two X values where the sine of X is equal to 1/3.

• These two values can be obtained by taking the inverse sine of 1/3 and subtracting it from or adding it to pi.