Trigonometry Beyond Triangles Concepts

The video tutorial introduces a new approach to trigonometry, expanding its use beyond right-angled triangles. It demonstrates how to calculate trigonometric functions like tan using given sine and cosine values without drawing triangles. The tutorial also explains how to determine the positivity of sine and cosine for angles using the unit circle, and provides examples to illustrate these concepts.

What is the main focus of the new foundation in trigonometry introduced in the video?

• Relying solely on right-angled triangles

• Expanding trigonometry beyond triangles

• Using only sine and cosine values

• Focusing on obtuse angles

In the first example, how is tan(a) calculated without using a triangle?

• By using the Pythagorean theorem

• By dividing sine by cosine

• By measuring angles directly

• By using a calculator

What does the video suggest about angles being positive or negative?

• All angles are positive

• Only acute angles are positive

• Angles can be positive or negative based on sine and cosine

• Only obtuse angles are negative

How is the positivity of sin(95) determined in the video?

• By using a calculator

• By checking the y-coordinate on the unit circle

• By drawing a right-angled triangle

• By measuring the angle with a protractor

What is the significance of the y-coordinate in determining sin(95)?

• It is irrelevant to the sine value

• It indicates the angle's size

• It shows the angle's position on the x-axis

• It determines if the sine value is positive or negative

In the third example, what is the method used to evaluate tan(153)?

• Using a calculator

• Analyzing the signs of sine and cosine

• Drawing a triangle

• Measuring the angle directly

What is the sign of sine at 153 degrees?

• Zero

• Positive

• Undefined

• Negative

What is the sign of cosine at 153 degrees?

• Undefined

• Zero

• Negative

• Positive

What is the result of dividing a positive sine by a negative cosine?

• Positive

• Negative

• Zero

• Undefined

What is the overall message of the video regarding trigonometry?

• Trigonometry is limited to triangles

• Trigonometry is only about sine and cosine

• Trigonometry is only about angles

• Trigonometry can be expanded beyond triangles