Trigonometric Functions and Quadrants

The video tutorial explains how to use the CAST diagram to determine the correct quadrant for drawing triangles based on given trigonometric information. It covers the process of identifying the quadrant using the sine value and angle range, drawing the triangle, and calculating the sides using the Pythagorean theorem. Finally, it demonstrates how to find the cosine value without a calculator.

What is the primary purpose of the CAST diagram in trigonometry?

• To determine the length of a triangle's sides

• To identify the sign of trigonometric functions in different quadrants

• To calculate the area of a triangle

• To find the hypotenuse of a right triangle

When the quadrant is not given, what method is suggested to determine it?

• Use a calculator to find the quadrant

• Guess based on previous questions

• Use the CAST diagram and given conditions

• Always assume the first quadrant

In which quadrants is the sine function positive?

• First and second quadrants

• Second and third quadrants

• First and fourth quadrants

• Third and fourth quadrants

What is the range of angles considered in the video for determining the quadrant?

• 180 to 360 degrees

• 90 to 360 degrees

• 90 to 180 degrees

• 0 to 90 degrees

Why is it important to draw the triangle in the correct quadrant?

• To make the triangle larger

• To ensure the triangle is a right triangle

• To avoid incorrect trigonometric calculations

• To simplify the calculations

What is the sine of theta given in the video?

• 3/4

• 4/5

• 3/5

• 5/3

What is the relationship between the opposite side and hypotenuse in the sine function?

• Opposite over adjacent

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Hypotenuse over opposite

How is the missing side of the triangle calculated using Pythagoras' theorem?

• By adding the squares of the other two sides

• By subtracting the square of one side from the square of the hypotenuse

• By multiplying the squares of the other two sides

• By dividing the square of the hypotenuse by one side

What is the value of the adjacent side in the triangle discussed?

• 5

• 3

• -4

• 4

What is the calculated value of cos(theta) in the video?

• 3/5

• -3/5

• 4/5

• -4/5