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This is going to require some visualization. Cosine is defined as the x-value on the unit circle.
If you picture where a point would be, for example, at the angle of pi/6 (30°) you get a coordinate of (√(3)/2 , 1/2) so cosine is √(3)/2 and sine is 1/2
To find a negative angle you take the reflection across the x-axis. Since this does not chance the x-value, only the y, cosine does not change. The coordinates of -(pi/6) (-30°) are (√(3)/2 , -1/2).
cos(-x) = cos(x)
sin(-x) = - sin(x)■
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What does sine times cosine equal?
Sin(x) cos(x) = 1/2 of sin(2x)
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.
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.
What is the formula for the y-intercept of a cosine function?
The Y-Intercept of the cosine function is X = 0, Y = cosine(0) = 1.
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
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.
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.
How do you differentiate a cosine function That is what is the derivative of the cosine of x with respect to the independent variable x?
The derivative of cosine of x is simply the negative sine of x. In mathematical terms f'(x) = d/dx[cos(x)] = -sin(x)
Does tangent of x equal cosine divided by sine?
No, it does not.
What is the anti derivative of negative cosine?
∫ -cos(x) dx = -sin(x) + C
What is the value of the angle in which the sine and cosine are equal and both negative?
225 degrees
What is the derivitive of a sine wave?
Negative cosine f(x) = sin(x) f'(x) = -cos(x)
What is the derivative of negative cosine?
The derivative of negative cosine is positive sine.
Can you make cosine squared X divided by2 equal to cosine squared x with some constant?
You could just pull out the half: it will be (1/2) cos squared x.
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.
What does sine times cosine equal?
Sin(x) cos(x) = 1/2 of sin(2x)
