Solving Trig Equations: Sections 7-8 Overview

The video tutorial introduces solving trigonometric equations, starting with basic concepts and moving to more complex problems. It highlights common issues with calculator outputs, particularly with inverse trigonometric functions, and explains the concept of one-to-one functions. The tutorial also covers the methodology for solving equations, including converting functions like cosecant to sine, and discusses the infinite nature of solutions in trigonometry. The video encourages active participation through a 'your turn, my turn' practice approach.

Why do calculators give unexpected results for trigonometric functions?

• None of the above

• Because they are not one-to-one functions

• Due to their one-to-one nature

• They pass the horizontal line test

What is the result of the inverse sine of square root of 2 over 2?

• 90 degrees

• 60 degrees

• 45 degrees

• 30 degrees

What does the calculator display when calculating the inverse sine of negative square root of 2 over 2?

• -90 degrees

• 45 degrees

• -45 degrees

• 90 degrees

What is the equivalent trigonometric identity for cosecant?

• cosine over sine

• sine over cosine

• 1 over sine

• 1 over cosine

What is the result of flipping both sides of the equation 1 over sine theta equals negative 2?

• Sine theta equals -1/2

• Sine theta equals 1/2

• Sine theta equals 2

• Sine theta equals -2

In which quadrants is sine negative?

• I and IV

• I and II

• II and III

• III and IV

What is the reference angle when sine is one half?

• π/2

• π/6

• π/4

• π/3

Why is it important to consider the range of 0 to 2π in trigonometric solutions?

• To simplify the calculations

• To ensure all possible solutions are considered

• To avoid negative angles

• To limit the solutions to one complete cycle

What additional term is added to account for multiple solutions in trigonometric equations?

• +/- 4πn

• +/- 3πn

• +/- 2πn

• +/- πn

How many solutions are possible for trigonometric equations involving sine and cosine?

• One

• A finite number

• Two

• An infinite number