#$&*
course mth 164
11;1o pm on June 22
8.1 problems9. 12^2 + 5^2 = c^2
144 + 25 = c^2
C = 13 hypotenuse
Sin theta = opp/hypotenuse = b/c= sin theta= 5/13
Cos theta= adjacent/hypotenuse = a/c = cos theta= 12/13
Tan theta = opp/adjacent = b/a = tan theta = 5/12
Csc theta = hypotenuse/opp = c/b = csc theta= 13/5
Sec theta = hypotenuse/adjacent= c/a = sec theta = 13/12
Cot theta = adjacent/opp = a/b = cot theta= 12/5
12. 3^2 + 3^2 = c^2
9 + 9 =c^2
18 = c^2
C= 4.24 hypotenuse
Sin theta = b/c = 3/3= sin theta =1
Cos theta = a/c= ¾.24 = cos theta = .708
Tan theta = b/a = 3/3 = tan theta = 1
Csc theta = c/b = 4.24/3 = csc theta = 1.413
Sec theta = c/a = 4.24/3= sec theta = 1.413
Cot theta = a/b = 3/3 = cot theta = 1
15. sin theta = b/c = sin theta = sqrt 6/3
Cos theta = a/c = cos theta = sqrt 3/3
Tan theta = b/c = tan theta = sqrt 2
Csc theta = c/b = csc theta = sqrt 6/2
Sec theta = c/a = sec theta = sqrt 3
Cot theta - a/b = cot theta = sqrt 2/2
19. sin 38 degrees - cos 52 degrees = 0
21. cos 10 degrees/ sin 80 degrees = 1
27. cos 35 degrees sin 55 degrees + sin 35 degrees cos 55 degrees = 1
@& It would be a good idea to explain how you reasoned out these last three. You could have plugged these quantities into a calculator (not a valid way to solve) or you could have used properties of the sine and cosine (e.g., cos(theta) = sin (90 deg - theta) so cos(10 deg) = sin(90 deg - 10 deg) = sin(80 deg), so cos(10 deg) / sin(80 deg) = 1).*@
29. b= 5, B = 20
A + B = 90 degrees, A + 20 degrees = 90 degrees, A = 70 degrees
Tan 70 degrees = a/2 = a = 6 tan 70 degree = 16.48
Cos 70 degrees = 2/c = c= 6/tan 70 degrees = 2.18
31. a= 6, B = 40 degrees Find b, c, and A
A + 40 degrees = 90 degrees, A = 50 degrees, b= 5.03, c= 7.83
37. c= 9, B= 20 degrees Find b, a, A. A + 20 = 90 degrees
A = 70 degrees, b= 3.08, a= 8.46
39. a =5, b= 3, find c, A, B.
A^2 + b^2 = c^2
5^2 + 3^2 = 34, c = 5.83
Tan A = a/b = 5/3
A= tan^-1(5/3)
A= 59 degrees (90-59) = B = 31 degrees
40. a= 2, b= 8, c, A, and B.
A^2 + b^2 = c^2
2^2 + 8^2 = 68, c= 8.25
Tan A = a/b = 2/8 = ¼, A= tan^-1 (1/4)
A= 14 degrees, (90-14= 76) , B = 76 degrees
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@& These look good, but I can't tell if you solved them all using appropriate methods. If you aren't sure, you're welcome to provide more detail and ask me to review your reasoning.*@