plz help with trigo?

Question

Find the value of:

log cot 28° 13’ 17”


2. Find the acute angle A, to the nearest second, when:
a. log cos A = 9.12575
b. log sin A = 9.91655

Answer 1

log(cot (28° 13’ 17”))

Under the assumption that log means log (base 10) then you need to convert degrees-minutes-seconds to decimal degrees, find the cotangent and then find the log (base 10). So,

(((17/60) + 13)/60) + 28 = 28.2214 (rounded to 4 decimal places.)
cot(28.2214) = 1.8633 (again rounded to 4 decimal places.)
log(1.8633) = .2703 (again rounded to 4 decimal places).

If by log you mean log (base 10) then there is no acute angle 'A' with the properties you requested. The maximum value the either the sin(x) or cos(x) reaches is 1. But the log(1) = 0. For all values of both sin(x) and cos(x) <= 0 the log(x) is not defined, and for values 0 < x < 1, the log(x) < 0, i.e. negative.

Did you mean ln(x) rather than log(x)?

HTH

Charles

Answer 2

log cot 28° 13’ 17” =
log(ctn(28 + (1/60)(13 + 17/60))) =
log(ctn( 28.2214) =
log(1.8633) = 0.27027
ln(1.8633) = 0.62236

2. Find the acute angle A, to the nearest second, when:
a. log cos A = 9.12575
b. log sin A = 9.91655

There is no such angle A that meets these conditions. Both sinA and cosA are ≤ 1.

Now, if
a. log cos A = 9.12575 - 10
cosA = 0.13358
A = ± 82.323° = 82° 46' 33"

b. log sin A = 9.91655 - 10
sinA = 0.82537
A = 55.626° = 55° 34' 35"