Trigonometric Ratios of Allied Angles

The video tutorial explains allied angles, which are angles whose sum or difference is a multiple of 90 degrees. It covers how to identify allied angles in both degrees and radians, and discusses their positions in different quadrants. The tutorial also explores the behavior of trigonometric functions for negative angles, highlighting which functions are even and which are odd. Finally, it explains how the quadrant of an angle affects the trigonometric ratios and how these ratios change when the angle is a multiple of 90 degrees.

What is the condition for two angles to be considered allied?

• Their sum or difference is a multiple of 360 degrees.

• Their sum or difference is a multiple of 180 degrees.

• Their sum or difference is a multiple of 90 degrees.

• Their sum or difference is a multiple of 45 degrees.

In which quadrant does the angle 180 minus theta lie?

• First quadrant

• Fourth quadrant

• Second quadrant

• Third quadrant

What is the sine of minus theta in terms of sine theta?

• -sine theta

• sine theta

• -cosine theta

• cosine theta

If theta is in the second quadrant, where does minus theta lie?

• Third quadrant

• Second quadrant

• First quadrant

• Fourth quadrant

Which trigonometric function is even?

• Tangent

• Sine

• Cosine

• Cosecant

What happens to the trigonometric ratio if the angle is an odd multiple of 90 degrees?

• The ratio changes from cotangent to cosecant.

• The ratio changes from tangent to secant.

• The ratio changes from sine to cosine and vice versa.

• The ratio remains the same.

How does the trigonometric function change if the angle is an even multiple of 90 degrees?

• The function changes from cotangent to cosine.

• The function changes from sine to tangent.

• The function changes from cosine to secant.

• The function does not change.