1. If sin 0= √2/2 Which could not be the value of 0
225∘
135∘
12∘
2. A gazebo is located in the center of a large, circular lawn with a diameter of 200 feet. Straight paths extend from the gazebo to a sidewalk around the lawn. If two of the paths form a 75° angle, how far would you have to travel around the sidewalk to get from one path to the other? Round your answer to the nearest foot if necessary.
a. 183 ft
b. 262 ft
c. 131 ft
d. 3,125 ft
3. A sine function can be used to model light waves. Green light has a wavelength, or period, of about 510 nanometers (nm). Which equations best model green light?
A y = sin π/225θ
By = sin 510/π θ
B y = sin π/255θ
1. To find the possible values for θ (0), we need to use the inverse sine function (sin⁻¹) on the given value (√2/2). This will give us the angle in radians.
sin⁻¹(√2/2) = π/4 radians
Now we convert this angle from radians to degrees:
(π/4) * (180/π) = 45 degrees
Therefore, the value of θ (0) cannot be 225°, as it is not equal to 45°.
2. To find the distance you would have to travel around the sidewalk from one path to the other, you can use the formula for the circumference of a circle.
Circumference = π * Diameter
Circumference = π * 200 ft
To find the distance between the two paths, we need to find the arc length of the sector created by the 75° angle. We can use the formula:
Arc Length = (Angle / 360°) * Circumference
Arc Length = (75° / 360°) * (π * 200 ft)
Arc Length ≈ 41.89 ft
Therefore, the distance you would have to travel around the sidewalk to get from one path to the other is approximately 41.89 ft.
3. The wavelength, or period, of green light is 510 nm.
The equation that models green light is:
y = sin [(2π / λ)θ]
where λ is the period or wavelength.
Substituting the given value:
y = sin [(2π / 510 nm)θ]
Therefore, the equation that best models green light is y = sin [(2π / 510)θ].