Understanding Quadrants and Trigonometric Functions

The video tutorial explains how to determine the quadrant of an angle's terminal side using trigonometric functions and the unit circle. It reviews the unit circle, showing how cosine, sine, and tangent relate to the circle's coordinates. The tutorial provides four examples, each demonstrating how to identify the quadrant based on given conditions for trigonometric functions like cosine, sine, tangent, secant, and cosecant. Each example is analyzed to determine the sign of the x and y coordinates, leading to the identification of the correct quadrant.

What information does the unit circle provide about trigonometric functions?

• It shows the values of sine and cosine for different angles.

• It helps in calculating the area of a circle.

• It provides the length of the radius of a circle.

• It determines the color of a circle.

If cosine theta is positive and sine theta is positive, in which quadrant is the angle?

• Quadrant 4

• Quadrant 1

• Quadrant 2

• Quadrant 3

When cosine theta is negative and sine theta is positive, which quadrant does the angle lie in?

• Quadrant 1

• Quadrant 3

• Quadrant 2

• Quadrant 4

If both x and y coordinates are negative, which quadrant is the angle in?

• Quadrant 1

• Quadrant 2

• Quadrant 4

• Quadrant 3

What does it mean if tangent theta is greater than 0?

• Both x and y are positive.

• Both x and y are negative.

• x is positive and y is negative.

• x is negative and y is positive.

Which trigonometric function is equal to y divided by x?

• Secant theta

• Sine theta

• Cosine theta

• Tangent theta

If secant theta is positive, what can be inferred about cosine theta?

• Cosine theta is negative.

• Cosine theta is undefined.

• Cosine theta is positive.

• Cosine theta is zero.

In which quadrant is the angle if x is positive and y is negative?

• Quadrant 4

• Quadrant 3

• Quadrant 2

• Quadrant 1

What is the reciprocal of cosine theta?

• Secant theta

• Cosecant theta

• Tangent theta

• Sine theta

If cosecant theta is negative, what can be said about sine theta?

• Sine theta is undefined.

• Sine theta is zero.

• Sine theta is negative.

• Sine theta is positive.