evaluate cos105 Degrees?

Question

using the additional formula

Answer 1

105 = 180 - 75
cos 105° is given by:-
cos (180 - 75)°
cos 180° cos 75° + sin 180° sin 75°
- cos 75°
- cos (45 + 30)°
- [ cos 45° cos 30° - sin 45° sin 30° ]
- [ (1/√2)(√3/2) + (1/√2)(1/2) ]
- [ (1/(2√2) ] [ (√3 + 1) ]

Answer 2

cos105 º = -0.25882
cos(45+60) = cos 45 cos 60 - sin 45 sin 60
= √ 2/2 (1/2) - √ 2/2 (√ 3/2)
= √ 2 /4 - √ 6/ 4
= -0.25882

Answer 3

105 degrees is in the second quadrant. Therefore the cos will be negative.

Cos 105 = cos (60 + 45) = cos60*cos45 - sin60*sin45 =

-(1/2 * 1/√2 - √3/2 * 1/√2) =

-(1/2√2 - √3/2√2)

= - (√3 -1)/2√2 = -.2588

Answer 4

Method I.
cos105
= cos(60+45)
= cos60 cos45 - sin60 sin45
= sqrt(2) [1 - sqrt(3)] / 4
= -.258819

Method II.
cos105
= cos(210/2)
= -sqrt[(1+cos210)/2]
= -sqrt[(1 - sqrt(3)/2)/2]
= -.258819

Answer 5

unit of angles is degrees,
cos 105
= cos (180 - 75)
= cos 180 cos 75 + sin 180 sin 75
= (-1) cos (45 + 30) + (0) sin (45 + 30)
= - (cos 45 cos 30 - sin 45 sin 30)
= - (((sqrt 2)/2)((sqrt 3)/2) - ((sqrt 2)/2)(1/2))
= (sqrt 2 - sqrt 6)/4
~= -0.25882.

Answer 6

cos (105) = cos(45+60) = cos 45*cos 60 -sin45 sin60=

1/2sqrt2 *1/2 -1/2 sqrt2* 1/2 sqrt 3= 1/4 sqrt 2(1-sqrt 3)

Answer 7

105 = 90 +15

use cos(90 +15) =
cos90 cos15 -sin90 sin15 = - sin15

sin(15) = sin(Pi/12 )= sin( Pi/3 -Pi/4) =

sinpi/3 cospi/4 - cospi/3 sinpi/4
sin(15) = (√3 /2 )(√ 2 /2) - (1/2)(√2 /2) =
√6 /4 -√2 /4 = (√6 - √2) /4
cos(105) = -sin(15) = (√2 - √6) /4

Answer 8

since cos(A+B) = cosA*cosB − sinA*sinB we could turn cos(105) into cos(60 + 45) since 60+45=105

now cos(60+45) = cos(60)*cos(45) − sin(60)*sin(45)
= 1/2*√2/2 - √3/2*√2/2 = (√2-√6)/4