arcsin(0.943)
= 1.23 ( in radian )
= 70.56 ( in degrees )
if tan x = cos x then sin x / cos x = cos x => sin x = cos x cos x => sin x = cos2 x => sin x = 1 - sin2x => sin2x + sin x - 1 = 0 Using the quadratic formula => 1. sin x = 0.61803398874989484820458683436564 => x = sin-1 (0.61803398874989484820458683436564) or => 2. sin x = -1.6180339887498948482045868343656 => x = sin-1 (-1.6180339887498948482045868343656)
tan(9) + tan(81) = sin(9)/cos(9) + sin(81)/cos(81)= {sin(9)*cos(81) + sin(81)*cos(9)} / {cos(9)*cos(81)} = 1/2*{sin(-72) + sin(90)} + 1/2*{sin(72) + sin(90)} / 1/2*{cos(-72) + cos(90)} = 1/2*{sin(-72) + 1 + sin(72) + 1} / 1/2*{cos(-72) + 0} = 2/cos(72) since sin(-72) = -sin(72), and cos(-72) = cos(72) . . . . . (A) Also tan(27) + tan(63) = sin(27)/cos(27) + sin(63)/cos(63) = {sin(27)*cos(63) + sin(63)*cos(27)} / {cos(27)*cos(63)} = 1/2*{sin(-36) + sin(90)} + 1/2*{sin(72) + sin(36)} / 1/2*{cos(-36) + cos(90)} = 1/2*{sin(-36) + 1 + sin(36) + 1} / 1/2*{cos(-36) + 0} = 2/cos(36) since sin(-36) = -sin(36), and cos(-36) = cos(36) . . . . . (B) Therefore, by (A) and (B), tan(9) - tan(27) - tan(63) + tan(81) = tan(9) + tan(81) - tan(27) - tan(63) = 2/cos(72) – 2/cos(36) = 2*{cos(36) – cos(72)} / {cos(72)*cos(36)} = 2*2*sin(54)*sin(18)/{cos(72)*cos(36)} . . . . . . . (C) But cos(72) = sin(90-72) = sin(18) so that sin(18)/cos(72) = 1 and cos(36) = sin(90-36) = sin(54) so that sin(54)/cos(36) = 1 and therefore from C, tan(9) – tan(27) – tan(63) + tan(81) = 2*2*1*1 = 4
x = sin-1 (4/15) ( sin -1 is [SHIFT] [sin] on a calculator ) = 15.5
sin x + csc x = 2 sin x + 1/sin x = 2 (sin2 x + 1)/sin x = 2/1 (cross multiply) sin2 x + 1 = 2sin x (subtract 2sin x to both sides) sin2 x - 2sinx + 1 = 0 (sin x - 1)2 = 0 (take the square root of both sides) sin x - 1 = 0 (add 1 to both sides) sin x = 1 x = sin-1 1 = 90⁰ 40x = 40(90⁰) = 3,600⁰ sin 40x = sin (3,600⁰ ) = 0 50x = 50(90⁰) = 4500⁰ sin 50x = sin (4,500⁰) = 0, so that csc 50x is undefined, we cannot divide by 0. Then, sin40x + csc50x is undefined.
1/sin x = csc x
943 = 1, 23, 41, 943
factors of 943 ----- 1, 23, 41, 943
1, 23, 41, 943
943 is an integer. It can be written, in fractional form, as 943/1 but I fail to see any situation when that would help.
157.1667
Passions - 1999 1-943 was released on: USA: 19 March 2003
943 thousandths in standard form is 9.43 × 10-1
Days of Our Lives - 1965 1-943 was released on: USA: 5 August 1969
Ryan's Hope - 1975 1-943 was released on: USA: 21 February 1979
Santa Barbara - 1984 1-943 was released on: USA: 29 April 1988
Late Night with Jimmy Fallon - 2009 1-943 was released on: USA: 20 May 2013
1035 - 943 = 92