Trigonometric Ratios and Special Angles

The video tutorial explains how to calculate sine, cosine, and tangent for special angles like 30, 60, and 45 degrees using a four-step process. It emphasizes the importance of memorizing two special triangles: one with angles of 45 degrees and another with 30 and 60 degrees. The tutorial demonstrates calculating the sine, cosine, and tangent of 210 degrees by drawing the angle on a grid, forming a triangle, and using the properties of special triangles. The process includes adjusting side lengths based on direction and verifying results with a calculator.

What is the first step in the four-step process for calculating trigonometric ratios for special angles?

• Memorize the special triangles

• Label the triangle

• Draw the angle on a grid

• Calculate the hypotenuse

Which of the following is NOT a special angle mentioned in the video?

• 90 degrees

• 60 degrees

• 30 degrees

• 45 degrees

What are the side lengths of the special triangle with two 45-degree angles?

• 1, 1, root 2

• 1, root 3, 2

• 1, 2, root 3

• root 2, root 2, 2

In the special triangle with angles 30 and 60 degrees, what is the length of the side opposite the 60-degree angle?

• 1

• root 3

• 2

• root 2

What is the angle difference between 210 degrees and 180 degrees?

• 45 degrees

• 30 degrees

• 15 degrees

• 60 degrees

In which quadrant does the angle 210 degrees lie?

• Second quadrant

• Fourth quadrant

• First quadrant

• Third quadrant

When drawing the triangle for 210 degrees, which side length is negative?

• Hypotenuse

• Side opposite 30 degrees

• Side opposite 60 degrees

• Both sides except hypotenuse

What is the sine of 210 degrees?

• root 3/2

• 1/2

• -1/2

• -root 3/2

What is the cosine of 210 degrees?

• -root 3/2

• 1/2

• root 3/2

• -1/2

What is the tangent of 210 degrees?

• -root 3

• root 3

• -1/root 3

• 1/root 3