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.
The true statements are Cosine is negative in Quadrant III. So option C is the correct one.
Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We know that
All the trigonometric ratios are positive in Quadrant I.
Sine is positive, cosine and tangent are negative in Quadrant II.
Tangent is positive, sine and cosine are negative in Quadrant III.
Cosine is positive, Tangent and Sine are negative in Quadrant IV.
Option (A) is Tangent is negative in Quadrant I. The statement is FALSE since all the ratios are positive in Quadrant I.
Option (B) is Sine is negative in Quadrant II. The statement is FALSE since Sine is positive in Quadrant II.
Option (C) is Cosine is negative in Quadrant III. The statement is TRUE since Cosine is negative in Quadrant III.
Option (D) is Sine is positive in Quadrant IV. The statement is FALSE since Sine is negative in Quadrant IV.
Thus, (C) is the correct statement.
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