Tangent Function Solutions and Properties

The video tutorial explains how to solve equations involving tan theta using graphs and calculators. It demonstrates finding solutions for tan theta equals one and root three, emphasizing the use of tan inverse and symmetry. The tutorial highlights the periodic nature of the tangent function and the importance of checking solutions with a calculator.

What is the first step in solving tan(theta) = 1 using a graph?

• Draw a line through y = 1

• Calculate the slope

• Identify the x-intercepts

• Use sine inverse

Which function is used to find the first solution for tan(theta) = 1?

• Cosine inverse

• Tangent inverse

• Sine inverse

• Cotangent inverse

What is the first solution for tan(theta) = 1?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

How do you find the second solution for tan(theta) = 1?

• Subtract 45 degrees from 270

• Add 90 degrees to the first solution

• Add 180 degrees to the first solution

• Multiply the first solution by 2

What is the second solution for tan(theta) = 1?

• 135 degrees

• 270 degrees

• 180 degrees

• 225 degrees

What is the approximate value of √3 used in the problem?

• 2.5

• 1.7

• 1.5

• 2.0

What is the first solution for tan(theta) = √3?

• 90 degrees

• 30 degrees

• 45 degrees

• 60 degrees

Why doesn't the method of subtracting from 270 work for tan(theta) = √3?

• The tangent function is not periodic

• The angle is too large

• The graph is not symmetrical

• The calculator gives an error

What is the correct second solution for tan(theta) = √3?

• 240 degrees

• 210 degrees

• 270 degrees

• 300 degrees

What property of the tangent function is used to find the second solution?

• Periodicity

• Symmetry

• Frequency

• Amplitude