Find the longitude and latitude for the points on the globe with angular coordinates ( θ , ϕ ) = ( π 4 , 11 π 12 ) (θ,ϕ)=(π4,11π12) and ( 4.6 , 2.8 ) . (4.6,2.8). (Round your answer to two decimal places. Assume 1 rad = 57.295 ∘ .)

For (45,165.02) Latitude and longitude is (45 0' 0",165 1' 12")

Hence latitude and longitude  are 4 degrees 35' 59.94" and 2 degrees 47' 59.994 "

Step-by-step explanation:

Given:

The angular coordinates  of the point on globe as (θ,∅)=(π/4,11π/12)

To find : longitude and latitude for this points:

Solution:

For finding this Longitude and latitude we should convert it into decimal degrees

Given that 1rad =57.295 deg.

we get for

θ=π/4

=3.142/4

=0.7855 *57.295

=45 degrees.

Now for φ=11π/12

=(11*3.142)/12=2.8801*57.295

=165.02 degrees

Now convert in longitude and latitude as ,

as degrees +min/60+seconds/3600

Now latitude =45 degrees

i.e. 45 degrees 0' 0"

And longitude as

165.02 degrees becomes

165 degrees 1' 12".

Hence For the angular co-ordinates (45,165.02)

Longitude and latitude is (45 0' 0",165 1' 12")

Now for the (4.6, 2.8)

we get using same

degrees+min/60+seconds/3600

=4 degrees 35' 59.94"

And for 2.8 means,  (similar to clock analog )

=2 degrees  47' 59.94"

Hence latitude and longitude  are 4 degrees 35' 59.94" and 2 degrees 47' 59.994 "

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x