Question

Which of the following is true?

Answer 1

Cosine is negative in Quadrant III. An easy way to remember the signs of the functions is ASTC or All Students Take Calculus. A: All functions are positive in quadrant I. S: Sine is positive in quadrant II. T: Tangent is positive in quadrant III. C: Cosine is positive in quadrant IV.

Answer 2

Answer:  The true statements are (C) Cosine is negative in Quadrant III.

Step-by-step explanation:  We are given to select the correct statement from the given options.

We know that

In Quadrant I -         all the trigonometric ratios are positive.

In Quadrant II -       Sine is positive, cosine and tangent are   negative.

In Quadrant III  -       Tangent is positive, sine and cosine are negative.

In Quadrant IV  -    Cosine is positive, Tangent and Sine are negative.

Option (A) is  

Tangent is negative in Quadrant I - FALSE, since all the ratios are positive in Quadrant I.

Option (B) is

Sine is negative in Quadrant II - FALSE, since Sine is positive in Quadrant II.

Option (C) is

Cosine is negative in Quadrant III - TRUE, since Cosine is negative in Quadrant III.

Option (D) is

Sine is positive in Quadrant IV - FALSE, since Sine is negative in Quadrant IV.

Thus, (C) is the correct statement.