Interpreting solutions of trigonometric equations | Trigonometry | Precalculus | Khan Academy

TL;DR

The video explains the function of a treadle and spinning wheel, and how to interpret the solution set of the given equations.

Transcript

• [Instructor] Alvaro presses the treadle of a spinning wheel with his foot. It moves a bar up and down making the wheels spin. So just to be clear what a treadle is this is an old spinning wheel and this little pedal that is a treadle. And as this goes up and down, it's gonna pull on this bar, which is then going to spin this wheel which can then ... Read More

Key Insights

• ✊ A treadle is a pedal that operates a spinning wheel, which can be used as a power source for various machines.
• 🤢 The function B(t) models the height of the top of the bar when the treadle has been pressed for t seconds.
• 🤢 Solution sets in equations represent specific heights of the top of the bar or moments in time when the height reaches a certain value.
• 🤢 The solution set for a specific value of t gives the height of the top of the bar at that time.
• 🤢 The solution set for a specific height value represents the times when the height of the top of the bar reaches that value.
• 🤢 The maximum height of the top of the bar occurs when sin(5t) equals 1 in the equation.
• 🤢 The minimum height of the top of the bar occurs when sin(5t) equals -1 in the equation.

Questions & Answers

Q: What does the solution set to y = 90 - 12sin(5*6) represent?

The solution set represents the height of the top of the bar when the treadle has been pressed for 6 seconds. It gives the vertical position at that specific time.

Q: What does the solution set to 95 = 90 - 12sin(5t) represent?

The solution set represents all the times (t) when the height of the top of the bar is equal to 95 centimeters. It indicates the moments when the bar reaches that specific height.

Q: What does the solution set to y = 90 - 12sin(pi/2) represent?

The solution set represents the lowest possible height of the top of the bar. Since sin(pi/2) equals 1, subtracting 12 times that results in the minimum value. It shows the bottommost position of the bar.

Summary & Key Takeaways

• The video demonstrates how a treadle operates a spinning wheel, which can be used to power a machine.

• The function B(t) models the height of the top of the bar when the treadle is pressed for t seconds.

• Questions include interpreting the solution set for specific values of t and understanding the maximum and minimum heights of the top of the bar.