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Suppose the performance starts at [tex]t = 0[/tex] seconds. At what times will the drone's altitude reach 500 feet during the first minute of the show?

Given the function: [tex]h(t) = 450 + 50 \sin \left( \frac{(t - 5) \pi}{20} \right)[/tex]

Answer :

The time at which the drone's altitude reach 500 feet is given by the equation T = 15 minutes

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the drone's height at 500 feet be represented as T

Now , the equation for drone's height is given by

h ( t ) = 450 + 50 [ sin ( t - 5 ) π/20 ] be equation (1)

where , h ( t ) is the height of drone

when height of the drone is at 500 feet

Substituting the value of h ( t ) = 500 in the equation , we get

500 = 450 + 50 [ sin ( t - 5 ) π/20 ]

On simplifying the equation , we get

Subtracting 450 on both sides of the equation , we get

50 = 50 [ sin ( t - 5 ) π/20 ]

Divide by 50 on both sides of the equation , we get

sin ( t - 5 ) π/20 = 1

From the trigonometric relations , sin 90° = 1

So , sin ( π/2 ) = 1

Substituting the values in the equation , we get

sin ( π/2 ) = sin ( t - 5 ) π/20

On further simplification , we get

( π/2 ) = ( t - 5 ) π/20

Multiply by 20 on both sides of the equation , we get

( t - 5 ) = 10

Adding 5 on both sides , we get

t = 15 minutes

Hence , the time required is 15 minutes to reach 500 feet

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