What is the Unit Circle? Part 2 | Don't Memorise

TL;DR

The unit circle helps us understand the relationship between angles and trigonometry functions, with sin+cos always equaling 1.

Transcript

this is where we left off in the previous video this is the unit circle with radius 1 and the origin as the center this length was sin Theta this length was cos Theta and the length of this tangent was tan Theta to understand the relation between the angle Theta and the functions let's try changing the angle Theta let me redraw the figure on a new ... Read More

Key Insights

• 🔨 The unit circle is a valuable tool in understanding the relationship between angles and trigonometric functions.
• 😇 As Theta increases, sin and tan increase while cos decreases in the first quadrant.
• 🥹 The trigonometric identity sin^2Theta + cos^2Theta = 1 holds true for any measure of Theta and any radius of the circle.

Questions & Answers

Q: What is the purpose of the unit circle in trigonometry?

The unit circle helps us visualize the relationship between angles and trigonometric functions by representing them as lengths on a circle with a radius of 1.

Q: How do sin, cos, and tan change as Theta increases in the first quadrant?

As Theta increases, sin and tan increase while cos decreases. This can be observed by changing the angle Theta and measuring the lengths on the unit circle.

Q: Can the trigonometric identity sin^2Theta + cos^2Theta = 1 be applied to circles with a different radius?

Yes, the trigonometric identity holds true regardless of the radius. For example, if the radius becomes 2, the identity becomes sin^2(2Theta) + cos^2(2Theta) = 1.

Q: What happens when Theta becomes 90° on the unit circle?

When Theta becomes 90°, the triangle formed on the unit circle collapses and the lengths of sin, cos, and tan cannot be defined in that position.

Summary & Key Takeaways

• The unit circle with a radius of 1 and the origin as the center helps us understand the relationship between angles and trigonometric functions.

• As the angle Theta increases, sin and tan increase while cos decreases.

• The Pythagorean Theorem applied to the unit circle gives us the important trigonometric identity sin^2Theta + cos^2Theta = 1.