Trigonometric Equations and Solutions

This video tutorial covers solving trigonometric equations using inverse functions, focusing on sine and cosine equations. It explains how to find solutions within a specified interval and discusses the general solutions for these equations. The tutorial also addresses more complex trigonometric equations involving substitutions and provides step-by-step solutions using calculators.

What is the primary method used to solve trigonometric equations in this video?

• Numerical approximation

• Algebraic manipulation

• Inverse trigonometric functions

• Graphical method

What is the first step in solving sin(x) = 0.48?

• Convert to degrees

• Use a calculator to find the angle

• Draw the unit circle

• Apply the inverse sine function

How many solutions are there for sin(x) = 0.48 in the interval [0, 2π]?

• Three

• Two

• One

• Four

What is the approximate value of the first solution for sin(x) = 0.48?

• 0.5065 radians

• 1.5708 radians

• 2.0944 radians

• 3.1416 radians

What is the method used to find the second solution for sin(x) = 0.48?

• Doubling the first solution

• Adding π to the first solution

• Using the cosine function

• Subtracting the first solution from π

What is the general solution for sin(x) = 0.48?

• x = 2.641 + 2πk

• x = 1.5708 + 2πk

• x = 0.5065 + 2πk

• x = 0.5065 + 2πk or x = 2.641 + 2πk

What is the equation being solved in the second example?

• tan(x) = 0.5

• cos(x) = -0.55

• sec(x) = 1.2

• sin(x) = 0.48

What is the first step in solving cos(x) = -0.55?

• Draw the unit circle

• Use a calculator to find the angle

• Convert to degrees

• Apply the inverse cosine function

How many solutions are there for cos(x) = -0.55 in the interval [0, 2π]?

• Four

• Three

• Two

• One

What is the approximate value of the first solution for cos(x) = -0.55?

• 3.1416 radians

• 1.5708 radians

• 0.7854 radians

• 2.153 radians