Trigonometric Functions and Their Applications

This video tutorial prepares students for an upcoming test by covering various mathematical concepts. It begins with an introduction to the lesson context during quarantine. The tutorial then explains how to find the area of a triangle using the Law of Sines and Cosines, and how to convert between degrees and radians. It also covers evaluating and graphing trigonometric functions, including sine, cosine, and tangent waves, with a focus on phase shifts and amplitude changes.

What is the main purpose of this lesson?

• To prepare students for an upcoming test.

• To introduce a new mathematical concept.

• To provide a fun activity during quarantine.

• To discuss the history of mathematics.

Which formula is used to find the area of a triangle when two sides and the included angle are given?

• The product of the sides divided by the angle.

• The sum of the squares of the sides.

• One-half the product of the two sides times the sine of the included angle.

• Base times height divided by two.

What is the law of sines used for in a triangle?

• To find unknown angles or sides in a triangle.

• To calculate the perimeter of the triangle.

• To determine the type of triangle.

• To find the area of the triangle.

How do you find an unknown angle using the law of cosines?

• By dividing the opposite side by the hypotenuse.

• By using the formula: side squared equals the sum of the other two sides squared minus two times the product of the two sides times the cosine of the angle.

• By subtracting the known angles from 180 degrees.

• By using the sum of the angles in a triangle.

How do you convert degrees to radians?

• Subtract 90 from the degree measure.

• Add 180 to the degree measure.

• Multiply by pi and divide by 180.

• Multiply by 180 and divide by pi.

In which quadrant is cosine positive?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the amplitude of a sine wave with a maximum of 2 and a minimum of -2?

• 2

• 4

• 3

• 1

How often does a tangent function repeat its cycle?

• Every pi

• Every 2 pi

• Every 3 pi

• Every 4 pi