It will be in 3rd Quadrant because cosine and sine both are negative in 3rd 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.
225 degrees
Sine(A+ B) = Sine(A)*Cosine(B) + Cosine(A)*Sine(B).
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.
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.
Sine is = to opposite side/hypotenuse, using a triangle with sides of opposite ~ 1, adjacent ~ 1 and hypotenuse ~ root(2), hypotenuse is always positive, hypotenuse = root(adjacent.squared * opposite.squared) if either is negative, squaring them brings it back to a positive and as the opposite side is the rise from the base line ( 0 degrees through to 180 degrees) it is positive in both quadrants 1 and 2 in quadrant 1, sine= 1/root(2) which is positive in quadrant 2, sine= 1/root(2) which is positive in quadrant 3, sine= -1/root(2) which is negative in quadrant 4, sine= -1/root(2) which is negative so sine is positive in quadrants 1 and 2 and is negative in 3 and 4
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.
When you subtract theta from 180 ( if theta is between 90 degrees and 180 degrees) you will get the reference angle of theta; the results of sine theta and sine of its reference angle will be the same and only the sign will be different depends on which quadrant the angle is located. Ex. 150 degrees' reference angle will be 30 degrees (180-150) sin150=1/2 (2nd quadrant); sin30=1/2 (1st quadrant) 1st quadrant: all trig functions are positive 2nd: sine and csc are positive 3rd: tangent and cot are positive 4th: cosine and secant are positive