A trough oflength L has a cross section in the shape of a semicircle with radius r. (See the accompanying figure.) When filled with water to within a distance h of the top, the volume V of water is V = L [O.Snr2 -r 2 arcsin(///r) - hir2 - h 2 ) i/2] .

Monday, October 3, 2016 Trigonometry, Week 6 2.5: Inverses of Circular Functions - Inverse Sine Function • x = sin y - y = arcsin (x) for -1 = x = 1 - y = sin ^-1 (x) for -pi/2 = x = pi/2 - Inverse Cosine Function • x = cos y - y = arccos (x) for -1 = x = 1 - y = cos ^-1 (x) for 0 = x = pi - Inverse Tangent Function • x = tan y - y = arctan (x) for x E all real numbers - y = tan ^-1 (x) for -pi/2 = x = pi/2 - Inverses of the Circular Functions • y = arcsin x —> sin y = x, -pi/2 = y = pi/2 • y = arccsc x —> cos y = x, -pi/2 = y < 0 or 0 < y = pi/2 • y = arctan x —> tan y = x, -pi/2 = y = pi/2 • y = arccot x —> cot y = x, 0 < y < pi • y = arccos x —> cos y = x, 0 = y = pi •