Trigonometric Graphs: Finding Multiple Solutions and Extending the Range

The video tutorial explains how to use trigonometric graphs to find multiple solutions for angles, emphasizing that these graphs extend beyond 0 and 360 degrees. It provides examples using cosine and tangent functions, demonstrating how to find equivalent angles and solutions within specified ranges. The tutorial highlights the symmetry of trigonometric graphs and their practical applications in solving equations.

What is the primary purpose of using trigonometric graphs in this lecture?

• To calculate the area under the graph

• To identify multiple solutions and extend graphs beyond standard ranges

• To determine the slope of the graph

• To find the exact value of angles

How is the cosine of 295 degrees related to an acute angle?

• Cos 295 is equal to Cos 25 due to symmetry

• Cos 295 is equal to Cos 45 due to symmetry

• Cos 295 is equal to Cos 65 due to symmetry

• Cos 295 is equal to Cos 85 due to symmetry

What is the significance of the symmetry in the cosine graph?

• It is irrelevant to trigonometric calculations

• It allows for the determination of equivalent angles

• It helps in finding the sine values

• It is used to calculate tangent values

What is the period of the tangent graph?

• 180 degrees

• 90 degrees

• 360 degrees

• 270 degrees

Which angle is NOT a solution for tan(theta) = 1 in the range -180 to 540 degrees?

• 135 degrees

• 225 degrees

• 405 degrees

• 45 degrees

How many solutions are there for tan(theta) = 1 in the range -180 to 540 degrees?

• Four

• Three

• Five

• Two

What is the key takeaway from the lecture regarding trigonometric graphs?

• They are only useful for small angle calculations

• They can be extended to find multiple solutions across various ranges

• They are primarily used for calculating sine values

• They are not applicable to real-world problems