Trigonometric Functions and Theorems

The video tutorial explains how to evaluate trigonometric functions for a given point (5, 12) by plotting the point, forming a right triangle, and using the Pythagorean theorem to find the hypotenuse. It covers calculating the sine, cosine, and tangent ratios, as well as their reciprocal functions: cosecant, secant, and cotangent.

What is the first step in evaluating trigonometric functions for a given point?

• Calculate the sine

• Plot the point and create a triangle

• Determine the reciprocal functions

• Find the hypotenuse

How do you plot the point 5, 12 on a graph?

• Move 5 units up and 12 units right

• Move 5 units right and 12 units up

• Move 12 units right and 5 units up

• Move 12 units up and 5 units right

What is the purpose of creating a right triangle when evaluating trigonometric functions?

• To calculate the perimeter of the triangle

• To establish a reference angle theta

• To determine the length of the hypotenuse

• To find the area of the triangle

Which theorem is used to find the hypotenuse of the triangle?

• Tangent rule

• Pythagorean theorem

• Sine rule

• Cosine rule

What is the length of the hypotenuse for the triangle with sides 5 and 12?

• 15

• 13

• 12

• 10

In the context of the triangle, what is the side opposite to angle theta?

• 5

• The hypotenuse

• 12

• 13

What is the adjacent side to angle theta in the triangle?

• 5

• 12

• The hypotenuse

• 13

How is the sine of angle theta calculated?

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Opposite over adjacent

• Hypotenuse over opposite

What is the cosine of angle theta in terms of the triangle sides?

• Hypotenuse over opposite

• Opposite over adjacent

• Opposite over hypotenuse

• Adjacent over hypotenuse

How is the tangent of angle theta determined?

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Opposite over adjacent

• Hypotenuse over opposite