Which of the following is true? tangent is negative in quadrant i. sine is negative in quadrant ii. cosine is negative in quadrant iii. sine is positive in quadrant iv.

 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.

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step-by-step explanation: