28 The Law of Sines: a/sin A = b/sin B = c/sin C 24/sin 42˚ = c/sin (180˚ - 42˚ - 87˚) since there are 180˚ in a triangle. 24/sin 42˚ = c/sin 51˚ c = 24(sin 51˚)/sin 42˚ ≈ 28
sin(0) = 0, sin(90) = 1, sin(180) = 0, sin (270) = -1 cos(0) = 1, cos(90) = 0, cos(180) = -1, cos (270) = 0 tan(0) = 0, tan (180) = 0. cosec(90) = 1, cosec(270) = -1 sec(0) = 1, sec(180) = -1 cot(90)= 0, cot(270) = 0 The rest of them: tan(90), tan (270) cosec(0), cosec(180) sec(90), sec(270) cot(0), cot(180) are not defined since they entail division by zero.
4 sin(x) - 3 = 0 Therefore sin(x) = 3/4 And so the primary solution is x = sin-1(3/4) = 49 deg The second solution in the domain is 180 - 49 = 131 deg.
By the sine rule, sin(C)/c = sin(B)/b so sin(C) = 25/15*sin(32d15m) = 0.8894 so C = 62.8 deg or 117.2 deg. Therefore, A = 180 - (B+C) = 85.0 deg or 30.5 deg and then, using the sine rule again, a/sin(A) = b/sin(B) so a = sin(A)*b/sin(B) = 28 or a = 14.3
To find which angle has a sine of 0.13, you calculate arcsin or sin^-1(0.13) =7.47 degrees 7.47 degrees has a sine of 0.13. There is also another angle , below 360 , has a sine of 0.13. Subtract 7.47 from 180. 180-7.47 = 172.53 degrees also has a sine of 0.13.
cot x = (cos x) / (sin x) cos (x - 180) = cos x cos 180 + sin x sin 180 = - cos x sin (x - 180) = sin x cos 180 - cos x sin 180 = - sin x cot (x - 180) = (cos (x - 180)) / (sin (x - 180)) = (- cos x) / (- sin x) = (cos x) / (sin x) = cot x
sin(-pi) = sin(-180) = 0 So the answer is 0
zero
For angles greater than 360 degrees, subtract multiples of 360 so that the relevant angle (the remainder) is between 0 and 360 degrees. Then For 90 < x ≤ 180 deg, sin(x) = sin(180-x) For 180 < x ≤ 270 deg, sin(x) = -sin(x-180) For 270 < x ≤ 360 deg, sin(x) = -sin(360-x)
If ø is an obtuse angle then (180 - ø) is an acute angle and: sin ø = sin (180 - ø) cos ø = -cos (180 - ø) tan ø = -tan (180 - ø)
cos(125) = cos(180 - 55) = cos(180)*cos(55) + sin(180)*sin(55) = -cos(55) since cos(180) = -1, and sin(180) = 0 So A = 55 degrees.
It is simply the sine of the supplementary angle. If x is an angle measuring (90, 180) degrees, then sin(x) = sin(180 - x).
sin(180) = 0 cos(180) = -1 tan(180) = 0 cosec(180) is not defined sec(180) = -1 cot(180) is not defined.
180 or pi...
28 The Law of Sines: a/sin A = b/sin B = c/sin C 24/sin 42˚ = c/sin (180˚ - 42˚ - 87˚) since there are 180˚ in a triangle. 24/sin 42˚ = c/sin 51˚ c = 24(sin 51˚)/sin 42˚ ≈ 28
Assuming the angles are expressed in radians:sin(5x) + sin(x) = 0∴ sin(5x) = -sin(x)∴ 5x = x + π∴ x = π/4On the other hand, if your angles are in degrees, then the answer would be:sin(5x) + sin(x) = 0∴ sin(5x) = -sin(x)∴ 5x = x + 180∴ x = 180°/4∴ x = 45°
It's not. The tangent of 180 degrees is zero. Consider tan(x) = sin(x)/cos(x). When x = 180 degrees, sin(x) = 0 and cos(x) = -1 and so tan(x) = 0