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The opposite leg, O, is approximately equal to the length of the blue arc, s. Gathering facts from geometry, s = Aθ , from trigonometry, sin θ = O / H and tan θ = O / A , and from the picture, O ≈ s and H ≈ A leads to: sin θ = O H ≈ O A = tan θ = O A ≈ s A = A θ A = θ . {\displaystyle \sin \theta ={\frac ...
An angle equal to 0° or not turned is called a zero angle. [ 5 ] An angle smaller than a right angle (less than 90°) is called an acute angle [ 6 ] ("acute" meaning " sharp ").
(If the inclination is either zero or 180 degrees (= π radians), the azimuth is arbitrary. If the radius is zero, both azimuth and inclination are arbitrary.) The elevation is the signed angle from the x-y reference plane to the radial line segment OP, where positive angles are designated as upward, towards the zenith reference.
Because the angle of the equilibrant force is opposite of the resultant force, if 180 degrees are added or subtracted to the resultant force's angle, the equilibrant force's angle will be known. Multiplying the resultant force vector by a -1 will give the correct equilibrant force vector: <-10, -8>N x (-1) = <10, 8>N = C.
The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as 0 kelvin (International System of Units), which is −273.15 degrees on the Celsius scale, [1] [2] and equals −459.67 degrees on the Fahrenheit scale (United States customary units or imperial units). [3]
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at
In contrast, by the Lindemann–Weierstrass theorem, the sine or cosine of any non-zero algebraic number is always transcendental. [4] The real part of any root of unity is a trigonometric number. By Niven's theorem, the only rational trigonometric numbers are 0, 1, −1, 1/2, and −1/2. [5]
In a vector space, the additive inverse −v (often called the opposite vector of v) has the same magnitude as v and but the opposite direction. [9] In modular arithmetic, the modular additive inverse of x is the number a such that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). [10]