The sine and cosine functions have several distinct characteristics: They are periodic functions with a period of 2π. The graph of y = sin x is symmetric about the origin, because it is an odd function. The graph of y = cos x is symmetric about the y-axis, because it is an even function.
Q. What quadrant is sin x 0 and cos x 0?
Quadrant IV
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Q. How is cos (- X COS X?
Since the cosine is the x-coordinate of the points on the unit circle, you see that the two points have the same cosine, and opposite sine. The cosine is an even function, which means exactly that cos(-x) = cos x.
Q. Does sin x cos x?
From the unit circle we see that sin x and cos x can only have the same value in two places, in x = /4 and x = 5 /4 (45° and 225°). The equation sin x = cos x can also be solved by dividing through by cos x. If we put k = 0 and k = 1 we get the solutions /4 (45°) and /4 + = 5 /4 (45°+ 180°= 225°).
Q. What is sin equal to in math?
Sine (sin) function – Trigonometry. In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. In any right triangle, the sine of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H).
Q. What is period of sin 3x 2?
Hence period of sin3x is 2π.
Q. What is the derivative of sin 3x?
We can find the derivative of sin(3x) (F'(x)) by making use of the chain rule….Using the chain rule to find the derivative of sin(3x)
| sin3x | ► Derivative of sin3x = 3cos(3x) |
|---|---|
| sin3x | ► Derivative of sin3x = 3cos(3x) |
| sin 3x | ► Derivative of sin 3x = 3cos(3x) |
| sin (3x) | ► Derivative of sin (3x) = 3cos(3x) |
Q. Why can’t you directly integrate sin 2x?
You cannot directly integrate sin^2(x). Use trigonometric identities and calculus substitution rules to solve the problem. Use the half angle formula, sin^2(x) = 1/2*(1 – cos(2x)) and substitute into the integral so it becomes 1/2 times the integral of (1 – cos(2x)) dx.
