arcus cosinus
http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
arc cos -0.32 is approx: --------------- | 108.66° | ---------------
Divide "1" by the argument "z" of the arcsec(z) function. Note, that "z" is equal to secant(angle) and 1/z is cosine (angle).For example, if arcsec(4) then cosine is "1/4" value or 0.25.Using a calculator, calculate the arccosine (arccos) function of "1/z" to get arcsec(z). Angle=arcsec(z)= arccos(1/z).In the example, arcsec(4)= arccos(0.25)=75.52 degrees.Calculate arcsecant if the function is given as arcsec(sec(Z)) e.g. arcsec(sec(45)). In such a case you do not need to calculate the secant value and then follow Steps 1 and 2. Instead, get an instant answer: arcsec equals Z. In this example, arcsecant of sec(45) is 45.
To find the angle between two vectors, you need to use this form: a ∙ b / (|ab|) = cos(θ) θ = arccos(a ∙ b / (|ab|)) where a and b are vectors. Compute the dot product and the norm of |a| and |b|. Then, compute the angle between the vectors.
If you have vectors U = (ai + bj + ck) and V = (di + ej + fk) and x is the angle between them, thencos(x) = U.V/(|U|*|V|)= (ad + be + cf)/[sqrt(a2+b2+c2)*sqrt(d2+e2+f2)]The angle x can be determined by calculating arccos of the above value.
Perhaps, related to "What is arccos(sqrt(Pi)/2)?" ... which is the trigonometric function that defines the vertex angle of a Pythagorean triangle that squares the circle: arccos(.88622692545275801364908374167057..) = 27.597112635690604451732204752339.. degrees. For a circle having a diameter equal to 2, the triangle's long side (circle's chord; side of its square) = sqrt(Pi) and its hypotenuse = 2 (circle's diameter), with the vertex point on the circumference.
0 is your answer tan(45)=1 and arccos(1)=0
arcsin(1) arccos(0)
f(x) = arccos(x) / 2 f'(x) = -1/(2√(1 - x2))
8
arc cos -0.32 is approx: --------------- | 108.66° | ---------------
Inverse of Cosine is 'ArcCos' or Cos^(-1) The reciprocal of Cosine is !/ Cosine = Secant.
I assume that you want to solve cos(x) = 2*pi, not pie! arccos(0.4) = 1.1593 radians. This is the solution in the range 0 to pi. There is another solution which is at 2*pi - 1.1593 = 5.1239 radians. Note that arccos appears on most calculators as "cos to the power -1".
Perhaps, related to "What is arccos(sqrt(Pi)/2)?" ... which is the trigonometric function that defines the vertex angle of a Pythagorean triangle that squares the circle: arccos(.88622692545275801364908374167057..) = 27.597112635690604451732204752339.. degrees. For a circle having a diameter equal to 2, the triangle's long side (circle's chord; side of its square) = sqrt(Pi) and its hypotenuse = 2 (circle's diameter), with the vertex point on the circumference.
To find the inverse cosine (arccos) on a TI-84 calculator, press the "2nd" button, then the "COS" button, which is located above the "COS" key on the calculator. This will bring up the arccos function. Enter the value for which you want to find the inverse cosine and then press "ENTER" to get the result. The answer will be displayed in radians by default; you can change the mode to degrees if needed.
Cos(x) equals zero at 90 degrees and 270 degrees. If x exceeds 360 degrees, cos(x) will equal zero at any increment of 90 + 180(n) degrees. In radians, this is equivalent to (pi/2) + pi(n) radians.
This would be the arccos(21/25), which is 32.859880378889108736588042568 degrees! lol