Principal Angles and Trigonometric Functions

Mrs. A explains how to solve for angle Theta using trigonometric ratios, focusing on the CAST rule to determine where the tangent ratio is negative. The video covers solving for Theta in both the fourth and second quadrants, converting negative angles to positive principal angles, and verifying solutions using a calculator.

What is the range of angles we are trying to find for Theta?

• 90 to 270°

• 180 to 360°

• 0 to 360°

• 0 to 180°

What does the CAST rule help us determine?

• The size of angles

• The type of triangle

• The positivity of trigonometric ratios in different quadrants

• The length of sides in a triangle

What is the significance of the CAST rule in trigonometry?

• It is used to calculate the area of triangles

• It helps in solving quadratic equations

• It helps in finding the hypotenuse of a triangle

• It determines the positivity of trigonometric functions in each quadrant

Which quadrant has all trigonometric ratios positive?

• First

• Third

• Fourth

• Second

In which quadrant is the cosine ratio positive?

• Second

• First

• Third

• Fourth

What is the first step in using the CAST rule?

• Find the cosine value

• Calculate the sine value

• Identify the quadrant

• Draw the angle

In which quadrants is the tangent ratio negative?

• Third and fourth

• First and third

• First and second

• Second and fourth

What is the first step in solving for Theta using the inverse tangent function?

• Calculate the cosine of the angle

• Draw the angle on a graph

• Use the calculator to find the inverse tangent

• Find the sine of the angle

What is the principal angle if the calculated angle is -49°?

• 229°

• 131°

• 311°

• 49°

What is the principal angle in the fourth quadrant if the related acute angle is 49°?

• 311°

• 229°

• 131°

• 49°