Question

A point on the unit circle lie on the terminal side of an angle in standard position quadrant IV.

Answer 1

The cosine of the angle is positive.

The sin of the angle is negative.

Explanation:

The problem is about a vector which is in quadrant IV, that is, its angles if from quadrant I to quadrant IV, this means that such angle is between 180° and 270°, because that's the range of angles placed on quadrant IV.

According to trigonometric function theory, in that quadrant, the cosine function of the angle is positive and the sine function of the angle is negative. This is because in the quadrant IV the independent variable is positive and the dependent variable is negative. The independent variable represents the cosine, and the dependent represents the sine.

Therefore, the complete sentences are

• The cosine of the angle is positive.
• The sin of the angle is negative.

Answer 2

The cosine of the angle is positive

The sine of the angle is negative

Explanation:

We are given that

angle lies in fourth quadrant

and we know that

In first quadrant:

sin is positive

cos is positive

In second quadrant:

sin is positive

cos is negative

In third quadrant:

sin is negative

cos is negative

in fourth quadrant , cosine of angle is always positive

and sine of angle is always negative

so,

The cosine of the angle is positive

The sine of the angle is negative