Sine is positive and cosine is negative in the second quadrant of the Cartesian coordinate system. In this quadrant, the angle is between 90 and 180 degrees, where the y-coordinate (sine) is positive and the x-coordinate (cosine) is negative. Thus, for any angle in the second quadrant, sine values are above the x-axis, while cosine values are below it.
It will be in 3rd Quadrant because cosine and sine both are negative in 3rd Quadrant
If (\cos(t) > 0), the terminal side of the angle (t) lies in the first or fourth quadrant. In the first quadrant, both cosine and sine are positive, while in the fourth quadrant, cosine is positive and sine is negative. Therefore, for angles where (\cos(t) > 0), the angle can be in either the first or fourth quadrant.
There's a mnemonic for this: All Students Take Calculus. Starting in the first quadrant, and moving counterclockwise until the last, give each quadrant the first letter of thos words in order. A represents all 3, s represents sine, t represents tangent, and c represents cosine. If the letter appears in a quadrant, it is positive there. If not, it is negative there.In quadrant 2, only sine is positive.
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
A 240-degree angle is an obtuse angle that measures more than 180 degrees but less than 270 degrees. It is located in the third quadrant of the Cartesian coordinate system, where both the sine and cosine values are negative. In terms of rotation, a 240-degree angle can be visualized as a clockwise turn from the positive x-axis, passing through the second quadrant and into the third quadrant.
All the angles in 4th quadrant have positive cosine and negative sine e.g. 280,290,300,310...etc.
The tangent function is equal to the sine divided by the cosine. In quadrant III, both sin and cos are negative - and a negative divided by another negative is positive. Thus it follows that the tangent is positive in QIII.
The derivative of negative cosine is positive sine.
It will be in 3rd Quadrant because cosine and sine both are negative in 3rd Quadrant
The negative sine graph and the positive sine graph have opposite signs: when one is negative, the other is positive - by exactly the same amount. The sine function is said to be an odd function. The two graphs for cosine are the same. The cosine function is said to be even.
If (\cos(t) > 0), the terminal side of the angle (t) lies in the first or fourth quadrant. In the first quadrant, both cosine and sine are positive, while in the fourth quadrant, cosine is positive and sine is negative. Therefore, for angles where (\cos(t) > 0), the angle can be in either the first or fourth quadrant.
To find the quadrant and sign of the cotangent function for -495 degrees, first, convert it to a positive angle by adding 360 degrees until the angle is within the standard range. -495 + 720 = 225 degrees. The angle 225 degrees is in the third quadrant, where both sine and cosine are negative, making cotangent (which is the ratio of cosine to sine) positive. Thus, cot(-495 degrees) is positive and located in the third quadrant.
There's a mnemonic for this: All Students Take Calculus. Starting in the first quadrant, and moving counterclockwise until the last, give each quadrant the first letter of thos words in order. A represents all 3, s represents sine, t represents tangent, and c represents cosine. If the letter appears in a quadrant, it is positive there. If not, it is negative there.In quadrant 2, only sine is positive.
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
The anti derivative of negative sine is cosine.
It doesn't really. Depending on the exact value of the argument, the cosine function can give both positive and negative results, for a negative argument. As to "why" the sine, or cosine, functions have certain values, just look at the function definition. Take points on a unit circle. The sine represents the y-coordinate for any point on the circle, while the cosine represents the x-coordinate for such a point. (There are also other ways to define the sine and the cosine functions.)
The angles in quadrant one measure between 0 degrees and 90 degrees. In radians, that's between 0 and pi/2. Quadrant one is the quadrant where both X and Y (or cosine theta and sine theta) are positive.