Trigonometric Functions and Their Applications

The video tutorial explains how to solve the trigonometric equation 1.2 cosine x equals sine 2x. It covers using a double angle identity for substitution, factoring the equation, and solving for cosine and sine. The tutorial identifies the two smallest positive solutions using a calculator and verifies them graphically. The solutions are approximately 0.644 radians and pi/2 radians.

What is the double angle identity used for sine 2x?

• sine 2a = sine a - cosine a

• sine 2a = 2 cosine a

• sine 2a = 2 sine a cosine a

• sine 2a = sine a + cosine a

What is the first step in factoring the equation 1.2 cosine x = 2 sine x cosine x?

• Subtract 1.2 cosine x from both sides

• Divide both sides by cosine x

• Multiply both sides by sine x

• Add 1.2 cosine x to both sides

When cosine x equals zero, what are the positive angles in radians?

• pi/4 and 3pi/4

• pi/3 and 2pi/3

• pi and 2pi

• pi/2 and 3pi/2

What is the approximate value of x when sine x equals 0.6?

• 2.498 radians

• 1.571 radians

• 0.644 radians

• 3.142 radians

How do you find the next positive solution for sine x = 0.6?

• Divide the reference angle by 2

• Multiply the reference angle by 2

• Subtract the reference angle from pi

• Add pi to the reference angle

What is the decimal approximation of pi/2?

• 2.498

• 3.142

• 1.571

• 0.644

Which tool is used to verify the solutions graphically?

• A protractor

• A graphing calculator

• A scientific calculator

• A ruler

What is the significance of x-intercepts in the graph of the equation?

• They represent the maximum points

• They represent the points of inflection

• They represent the solutions to the equation

• They represent the minimum points

What is the exact value of the second smallest positive solution?

• 3pi/4

• pi

• pi/2

• pi/4

What does the graph confirm about the equation's solutions?

• There are no solutions

• There are only two solutions

• There are infinite solutions

• There is only one solution