Trig Honors extra credit

Trigonometric Functions

100

convert and solve sin 49^o12^'

49 12^o/60=49.2^o 

sin 49.2^o=0.76

200

solve with the cos function

adjacent= 25

hypotenuse= 50

25/50= 0.5

300

find the degree 

opposite = 1.4433756 m

adjacent = 2.5 m

1.4433756/2.5 = (√3)/3

tan^-1 ((√3)/3)=30^o

400

verify cot s + 1= csc s(cos s + sin s)

1/sin s (cos s + sin s)=

(cos s/sin s) + (sin s/sin s)=

 cot s + 1

 cot s + 1= cot s + 1

500

find the identity of sin x in the equation: cos 2x= 1 - 2sin²x

(cos 2x= 1 - 2sin²x)-1

(-1 + cos 2x= -2sin²x) * -1

(1 - cos 2x= 2sin²x)/2

√(1-cos⁡2x)/2 = sin x

angles

100

find the angle of X when the other two angles in the triangles are 87^o and 29^o

87^o + 29^o = 116^o

180^o - 116^o = 64^o 

x=64^o

200

convert 51^o42'

42/60=0.7 

51.7^o

300

find the radian of 150^o

150/180= 5/6

5π/6

400

convert 12π/13 to degrees

12π/13 x 180/π= 166.15^o

500

A ship travels 50km at an angle of 27^o , then travels at a bearing of 117^o for 140km. find the distance between its end point and start point?

140km/sin(63^o)=157.1km

Graphs of sines and cosines

100

find the coordinates of y=sine x 

       x l y

   0     l 0

   .7     l π/4 

    1     l π/2

    .7    l 3π/4

    0     l π

    -.7   l 5π/4

200

Find the coordinates of y=sin7x

    x /7 l y

   0      l 0

   0.1   l π/4 

    1/7  l π/2

    0.1  l 3π/4

    0     l π

    -0.1 l 5π/4

300

find the coordinates of y=3cosx

    cos  l 3x

    1     l 0

   .7     l 3π/4 

    0     l π/2

    -.7   l 3π/4

     -1   l π

    -.7   l 5π/4

400

find the coordinates of y=5 sin 4(x)

  x/4   l 5*y

   0     l 0

   .125 l 5π/4 

    4     l 5π/2

   .125 l 15π/4

    0     l 5π

  -.125 l 25π/4

500

find the coordinates of y=3+2cos4(x-6)

 x/4 + 3 l 2*y+6

     3   l 6

 3.175 l 7.6

  3.25  l 9.1

 3.175 l 10.7

    3     l 12.3

 2.825  l 5π/4

applying trig and vectors

100

solve b if A=32^o, B=81.8^o, and a=42.9 cm

42.9 * sin(81.8^o )=42.5

42.5/sin(32^o)=80.1 cm

80.1 cm=b

200

Find ABC if B=42^o, a=12 cm, b=20 cm

sin(42^o)*12=8.03

8.03/20=0.4

sin^-1(0.4)=23.67^o

180^o-(42^o + 23.67^o )=114.33^o

300

find the area of a triangle that has had the side lengths of a=29.7 feet, b=42.3, c= 38.4

.5(29.7+42.3+38.4) = 55.2

√55.2(55.2-29.7)(55.2-42.3)(55.2-38.4) =552ft²

400

find the vectors of lvl and lul when lwl = 25 and thier is a degree of 40^o

sin(40^o)*25= 16.07=lvl

cos(40^o)*25= 19.15=lul

500

Two tracking stations are on an east-west lime 110 miles apart a forest fire is N 42^o E from the western station and N  15^o E from the eastern station. how far is the fire from the western station?

90^o-42^o=48^o, 90^o+15^o=105^o, 180^o-105^o-48^o=27^o

sin(105^o)*110=106.3

106.3/sin(27^o)

complex numbers

100

solve x²=-9

x²=-9

x=-√-9

x=-i√-9

x=-3i

200

solve √-2 * √-32

 √-2 * √-32= i√2 * i√32

=i²√64

=(-1)8

=-8

300

solve (3-4i) + (-2 + 6i)

(3-4i) + (-2 + 6i)= (3+(-2)) +(-4+6)i

=1+2i

400

solve (3-i)(3+i)

(3-i)(3+i)=9+3i-3i-i²= 9-(-1)=10

500

solve 2(cos 300^o + i sin 300^o)

2(cos 300^o + i sin 300^o)=2(1/2-i√3/2)=1-i√3