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What is the difference between negative sine and cosine graphs and positive sine and cosine graphs?
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.
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Why is the tangent positive on quadrant III?
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.
Why the value of cos positive for negative value of angle?
The cosine of an angle is the adjacent side of the angle of a triangle divided the hypotenuse. If you plot the adjacent side as x on an x -y graph, for negative angles less than 90 degrees the adjacent side is positive and the hypotenuse is always positive, so you get a positive. The cosine is positive int e upper right and lower right quadrants
Is the cosine function an odd function?
No. Cosine, along with sec, is an even function. The odd functions are sin, tan, csc, and cot. The reason for this is because is you take the opposite of the y-value for the cosine function, the overall value of the function is not affected.Take, for example, cos(60 degrees), which equals POSITIVE 1/2.If you flip it over the x-axis, making the y's negative, it becomes cos(-60 degrees), or cos(300 degrees). This equals POSITIVE 1/2.Now let's look at an odd function. For example, sin(30 degrees) equals POSITIVE 1/2. Now take the opposite of this.sin(-30 degrees), or sin(330 degrees), equals NEGATIVE 1/2. This is because it is found in the fourth quadrant, where the y's are negative. Sine of theta, by definition, is y divided by r. If y is negative, sine is negative.
What is the difference between a sine graph and a cosine graph?
The sine graph and the cosine graph are identical in shape, with the cosine graph shifted to the left by pi / 2, i.e. the sine starts at (x=0,y=0) and proceeds up with an initial slope of one, and the cosine starts at (x=0,y=1), and proceeds down with an initial slope of zero.
How do you find amplitude in trigonometry?
The amplitude of a sine (or cosine) curve is the difference between the maximum and minimum values of the curve, measured over a whole cycle.
What is the derivative of negative cosine?
The derivative of negative cosine is positive sine.
Why are cosines positive and negative?
Because the cosine of some angles is positive and the cosine of some other angles is negative.
Which angle has a negative sine and a positive cosine?
All the angles in 4th quadrant have positive cosine and negative sine e.g. 280,290,300,310...etc.
What is the answer to cosine x equal to negative one?
cosine(x) = -1x = (270 + 360N) degreesorx = (1.5 + 2N) pi radiansN is any integer, positive or negative.
Why is cosine 16 negative?
First of all, I can't tell what angle you're talking about, because you failedto mention the unit of your angle.-- Cosine of 16 degrees is roughly 0.9613 ... a positive number.-- Cosine of 16 radians is roughly -0.9577 ... a negative number.-- Cosine of 16 grads is roughly 0.9686 ... a positive number.Over any reasonably large range of angles, half of them have positive cosines,and the other half of them have negative cosines.
Why is the tangent positive on quadrant III?
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.
Why cos negative results positive?
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.)
What is cos of a negative angle?
The cosine function is an even function which means that cos(-x) = cos(x). So, if cos of an angle is positive, then the cos of the negative of that angle is positive and if cos of an angle is negative, then the cos of the negative of that angle is negaitive.
Why do cosine to the negative 1th power and cosine cancel out each other?
Cosine to the negative first power and cosine cancel each other out because cosine to the negative first power is one over cosine, and one over anything times anything is just one.
Why the value of cos positive for negative value of angle?
The cosine of an angle is the adjacent side of the angle of a triangle divided the hypotenuse. If you plot the adjacent side as x on an x -y graph, for negative angles less than 90 degrees the adjacent side is positive and the hypotenuse is always positive, so you get a positive. The cosine is positive int e upper right and lower right quadrants
Does cos x equal cos negative x?
Yes. Cosine is adjacent side over hypothenuse. Adjacent side is the same sign when x is positive or negative.
Why does cos negative theta equal cos postitive theta?
The cosine is simply the x-coordinate of the unitary circle. It helps to draw the circle, and the sine and cosine (x and y coordinates), to visualize this. The y-coordinate is the same for a positive angle and for the corresponding negative angle.
