Small Angle Approximations in Trigonometry

The video tutorial explains the concept of ratios and how small angles behave similarly in trigonometric functions like sine and tangent. It demonstrates how to use these approximations in practical measurements, such as calculating the height of a distant tower using trigonometry. The tutorial also provides a visual explanation of the relationship between sine and theta, emphasizing the similarity between the arc and chord lengths for small angles.

What does it mean when the ratio between two quantities is one?

• The two quantities are different in size.

• The two quantities are the same size.

• One quantity is twice the size of the other.

• The two quantities are unrelated.

For small angles, which two trigonometric functions are approximately equal?

• tan(Theta) and Theta

• sin(Theta) and Theta

• tan(Theta) and cos(Theta)

• sin(Theta) and cos(Theta)

How does cosine behave for small angles?

• cos(Theta) is approximately equal to Theta.

• cos(Theta) is approximately equal to sin(Theta).

• cos(Theta) is approximately equal to zero.

• cos(Theta) is approximately equal to one.

What is the significance of the limit of cos(Theta) for small angles?

• It approaches zero.

• It approaches Theta.

• It approaches one.

• It approaches infinity.

What is the first step in using small angle approximations for practical measurements?

• Ignore the angle's unit.

• Use the angle directly in degrees.

• Convert the angle from degrees to radians.

• Convert the angle from radians to degrees.

In the example provided, what is the distance from the observer to the tower?

• 20 km

• 10 km

• 15 km

• 18 km

What is the approximate height of the tower calculated using small angle approximation?

• 314 meters

• 315 meters

• 316 meters

• 317 meters

Why is it important to convert degrees to radians in trigonometric calculations?

• Radians are easier to understand.

• Degrees are not used in mathematics.

• Radians are larger than degrees.

• Radians are the standard unit for trigonometric functions.

What is the relationship between the arc length and chord length for very small angles?

• The arc length is unrelated to the chord length.

• The arc length and chord length are approximately the same.

• The arc length is much shorter than the chord length.

• The arc length is much longer than the chord length.

What does the visual explanation of sin(Theta) and Theta demonstrate?

• The difference between sin(Theta) and cos(Theta).

• The similarity between the arc and chord for small angles.

• The difference between radians and degrees.

• The relationship between tan(Theta) and Theta.