Trigonometric Ratios and Definitions

The video tutorial explains trigonometric ratios using right-angled triangles and extends these definitions to the Cartesian plane, allowing for any angle. It introduces the concept of using a circle centered at the origin to define trigonometric ratios in terms of x, y, and r. The tutorial also covers the general definitions of sine, cosine, and tangent, and relates them to the SOHCAHTOA rule, providing a method to remember these ratios using the Cartesian plane.

What is the primary difference between defining trigonometric ratios using right-angled triangles and the Cartesian plane?

• Right-angled triangles use angles, Cartesian plane uses coordinates.

• Right-angled triangles are only for acute angles, Cartesian plane is for any angle.

• Right-angled triangles use coordinates, Cartesian plane uses angles.

• Right-angled triangles are for obtuse angles, Cartesian plane is for acute angles.

How is the radius of the circle defined in the context of trigonometric ratios on the Cartesian plane?

• As the distance from the origin to point P.

• As the distance from the origin to the x-axis.

• As the distance from point P to the y-axis.

• As the distance from the x-axis to the y-axis.

In the circle centered at the origin, what does the length 'y' represent?

• The distance from the origin to the x-axis.

• The radius of the circle.

• The distance from the x-axis to point P.

• The distance from the y-axis to point P.

How is sine theta defined in terms of x, y, and r?

• x over r

• x over y

• y over r

• y over x

What is the formula for cosine theta in terms of the circle's components?

• r over x

• y over x

• y over r

• x over r

Which trigonometric ratio is defined as y over x?

• Sine theta

• Cotangent theta

• Cosine theta

• Tangent theta

What does the SOHCAHTOA rule help you remember?

• The definitions of the sides of a triangle.

• The definitions of secant, cosecant, and cotangent.

• The definitions of angles in a triangle.

• The definitions of sine, cosine, and tangent.

According to SOHCAHTOA, what is the relationship for cosine?

• Opposite over adjacent

• Hypotenuse over adjacent

• Adjacent over hypotenuse

• Opposite over hypotenuse

In the context of the Cartesian plane, which side is considered adjacent to angle theta?

• The x-coordinate

• The radius of the circle

• The hypotenuse

• The y-coordinate