Trigonometry questions please review the answer and do the remaining questions

TRIGONOMETRY

1. Multi STEP Problem

Given:

Length=800ft

Angle of elevation=30 degrees

Speed=320ft per meter

a. Sin 30=

In this case the length is the hypotenuse and the height is the opposite

Hence the Length is calculated as= 800sin30

Length=400 meters

b. Speed is a vector; hence it must have a vertical and horizontal component.

Assuming that vertical speed is “a”, applying the sin formula, we have =sin 30

a=320sin 30=160ft/meter

2. Multi Step Problem

a. To calculate x, we can apply the trigonometric equations

We have the height =45 (opposite of the angle 25 degrees), and the and the angle

Hence sin (25) =

X=

X=106.48 ft

b. How far apart are the poles holding the cable= in this case we are being asked to calculate the adjacent of the angle 25 degrees

We can apply the tangent rule

Tan (25)=

The adjacent=

The distance between the poles =96.5ft

3. Gridded Answer

boulder

stake 70m

the distance between the stake and boulder represent the width of the river and also represecent the opposite of the angle

Hence tan (67)=

Width of the river =opposite distance=70tan (67)

=164.91=165 meters

4. 300 degrees

5. In the third gear, the gear ratio is. For every one turn of the chain wheel in this gear the freewheel makes 1.091 rotations. The number of the angle θ through which the free wheel turns when the chain wheel completes 4 rotations is:

Θ=(4.3636 rotations)(1570.9 degrees

To find the angle measure in radians, multiply by

Θ=1570.9=27.42 radians

c. If the chain wheel makes 3 rotations:

3=3.2727 rotations

Θ=3.2727 rotations

Θ=1178.2 degrees

The angle is smaller

6.

θ	25	30	35	40	45	50	55	60	65
d	264	298	324	339	345	339	324	298	264

In this case is constant. Hence the distance d comes from sin2θ multiplied by the constane

B. The value which maximizes the horizontal distance is obtained at sin 90

2θ=sin90

Θ=45 degrees

PART 2

1. From the sine equation: h=2sint+4

is the period

quency=1/period

=frequency

2. The frequency=5hz

5=b/2π

b=10π h=100sin10πt

When depth will be 5ft

H=5=100sin10πt

T=0.01 seconds

3. D=27Sin(t-1.3):t=1

D=-O.6

4.

5. frequency=

Period=

1/10=

b=20π

Maximum height is 12,a=12

y=12sin20t

IT is a sine curve since b

6. THE AMPLITUDE=

Vertical distance=6-2=4

Horizontal distance=0-4=-4

===

Amplitude is= 5.656 units

7. tanθ=

d=300-80tanθ

Domain=d

Intercept= (0,0)