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In which quadrants is sin(theta) < 0?

In which quadrants is cos(theta > 0?
In which quadrants is tan(theta) < 0?

consider angles in standard position.

sinθ = y/r
cosθ = x/r
tanθ = y/x
so, sinθ < 0 when y < 0 -- QIII,QIV
now do the others

Did you know?

Did you know that in trigonometry, the sine of an angle (sin(theta)) is negative in the third and fourth quadrants? This means that if you measure an angle and calculate its sine value, and it is less than zero, the angle lies either in the third or fourth quadrant on the unit circle. Similarly, the cosine of an angle (cos(theta)) is positive in the first and fourth quadrants. So, if you find that the cosine value of an angle is greater than zero, the angle is located in either the first or fourth quadrant on the unit circle. Furthermore, the tangent of an angle (tan(theta)) is negative in the second and fourth quadrants. Hence, if you determine that the tangent value of an angle is less than zero, it indicates that the angle falls in either the second or fourth quadrant on the unit circle. Understanding the behavior of these trigonometric functions in different quadrants can help to locate angles in the Cartesian coordinate system and solve various mathematical and real-world problems.