Problems need checking: Right Triangles, bearings,h. motion, & App. w/ Triangles

I have some problems, i have completed that needs to be checked.

__Solving Right Triangles: __

I'm given a right triangle where the outer points are a,b,c, and the angles inside the triangles, are A,B,C.

1. A = 41.5 degree, b = 20

20 tan (41.5 degrees) = 17.69 a

20/cos (41.5) = 26.70 c

48.5 B

2. A = 54.8 degrees, c = 80

35.2 degrees B

80 sin (54.8 ) = 65.37 b

6400-4225 = 21751 square equals 46.63 a

4. a = 11.2, c = 65.8

11.2 ^ 2 + b ^ 2 = 65. 8 ^ 2

4329.64

-125.44

-----------

4204.20 squared is 64.83 for b

sin-1(11.2/65.8) = 9.80 for A

80.2 degrees for B

5. 15.3 , b = 17.6

234.09 + 309.76 = 543.85 squared is 23.32 for c

tan -1 (17.6/15.3) = 49 degrees for A

41 degrees for B

6. b = 4, c = 9

9 ^ 2 - 4 ^ 2 =

81 - 16 = 65 a

cos -1 (4/9) = 63.61 degrees for A

26.39 degrees for B

Bearings:

N 60 degrees (B) W , N 75 degrees (A) E , W 80 degrees (C) S, S 35 degrees (D) E

Find the bearing from O to B (O is the origin)

N 30 degrees W

Find the bearing from O to D

S 55 degrees E

Harmonic Motion (Equations):

An object is attached to a coiled spring. The object is pulled down (neg. direction from the rest position) and then released. Write an equation for the distance of the object from its rest position after t seconds

8 inches ( Distnace ) 6 cent (Amp.) 4 (secs)

- 8 cos PI t

For this one, the object is propelled downward from its rest position at time t = 0. Write an equation for the distance of the object from its rest position after t seconds

Distance: 0 cent amp: 5 cent 2.5 secs.

* I'm not sure about my answer for B. This is what i came up with:

2 PI / 2.5 x 2/2 = 4 PI/5

Answer: 5 sin 4 PI /5

For these I'm given the equations, and i have to figure out the:

Displacement Max.

frequency

Time for one cycle.

1. d = 10 cos 2 PI t

Displacement: 10

freq. 2 PI / 2 PI x 1 / 2 PI = 1 per sec

1 sec (period)

2. d = - 8 cos PI/2 t

Displacement: 8

freq. PI / 2 / 2 PI x 1 /2 PI = 1 per sec

1 sec (period)

3. d = 1/3 sin 2 t

1/2 displacement

1/ 2 PI per sec

2 PI period

** I'm still working on some, so i'll try posting them up as i complete each section.