Trigonometric Functions and Angles

Anil Kumar explores trigonometric ratios in the Cartesian plane, focusing on angles between 0 and 360 degrees. The video demonstrates how to find two angles with the same sine, cosine, or tangent values using special triangles and calculators. It explains the properties of trigonometric functions in different quadrants and provides practical examples to reinforce the concepts. The video concludes with test questions to apply the learned concepts.

What is the range of angles considered in the Cartesian plane for trigonometric ratios?

• 0 to 360 degrees

• 0 to 180 degrees

• 0 to 90 degrees

• 0 to 270 degrees

Which two angles have the same sine value as 60 degrees?

• 180 degrees and 270 degrees

• 120 degrees and 240 degrees

• 120 degrees and 300 degrees

• 150 degrees and 210 degrees

In which quadrant is the sine function positive?

• Quadrant I and IV

• Quadrant III and IV

• Quadrant II and III

• Quadrant I and II

Which two angles have the same cosine value as 30 degrees?

• 90 degrees and 270 degrees

• 30 degrees and 330 degrees

• 60 degrees and 300 degrees

• 150 degrees and 210 degrees

In which quadrants is the cosine function positive?

• Quadrant I and IV

• Quadrant II and III

• Quadrant I and II

• Quadrant III and IV

Which two angles have the same tangent value as 20 degrees?

• 200 degrees and 340 degrees

• 160 degrees and 340 degrees

• 200 degrees and 320 degrees

• 180 degrees and 360 degrees

In which quadrants is the tangent function positive?

• Quadrant II and IV

• Quadrant I and III

• Quadrant III and IV

• Quadrant I and II

What is the principal angle for an acute angle of 30 degrees in the third quadrant?

• 240 degrees

• 210 degrees

• 270 degrees

• 300 degrees

Which angle is equivalent to 45 degrees in the fourth quadrant?

• 405 degrees

• 225 degrees

• 135 degrees

• 315 degrees

What is the importance of using special triangles in trigonometry?

• They simplify calculations without a calculator.

• They are only used for angles above 180 degrees.

• They are not useful in the Cartesian plane.

• They are only applicable in the first quadrant.