[notes : i cannot use the symbol for pi or epsilon, so i have used the word pi instead and the letter e instead]
 
 

1. Solve the triangle BGT, if B = 20°, T = 90°, and t = 18.6.

Angle G
B + G + T = 180
(20) + G + (90) = 180
G = 70

Side b
sin b = opp/hyp
sin20° = ^b / _18.6
b = 6.4

Side g
cos g = ^adj/_hyp
cos 20° = ^g / _18.6
g = 17.5

CHECK
t² = b² + g²
(18.6)² = (6.4)² + (17.5)²
345.96 = 347.21

2. Solve the triangle WAM, if W = 90°, a = 48.5, m = 18.3.

Side w
w² = a² + m²
w²  = (48.5)² +(18.3)²
w²  = 2687.14
w = 51.8

Angle M
tan M = ^opp / _adj
tan M = ^18.3 / _48.5
M = 21°

Angle A
tan A = ^opp / _hyp
tan A = ^48.5 / _18.3
A = 69

CHECK
M + A + W = 180
(21) + (69) + (90) = 180
180 = 180

3. Solve for all possible k.  Give your answer in radians.

 3cos²k + 13cosk + 4 = 0

(3cosk + 1)(cosk + 4) = 0

If
3cosk + 1 = 0
cos k = ^-1/₃
cos is negative, therefore quadrants 2 and 3. (YOU SHOULD BE DRAWING A DIAGRAM HERE)
cos^-1  (¹/₃) = 1.231  ( note since we already have considered the negative aspect of ^-1/₃, here we just use ¹/₃.
therefore, in quadrant 2,
** k = pi - 1.231 = 1.911
and in quadrant 3,
** k = pi + 1.231 = 4.373.

If
cosk + 4 = 0
cox k = -4
** therefore no solutions.

THEREFORE,
k = 1.911 + 2(pi)n, n e I, or
k = 4.373 + 2(pi)n, n e I.
 




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