What's the best way to find Angles using logarithms and vice-versa.

Ex: log cot 0.1690 and log sin (25degrees 22min)

log sin (25+22/60)
= log sin 22.3666666667
= sin 0.38053243281
= (-0.41960832236)

Is there a simpler way to do these?

I get confused with finding the angles using logarithms

nope. to take the log, ya gotta find the sine first.

Of course, if you have a decent calculator, that means you just have to

enter 22/60+22=
then press deg sin log

But how can you do the inverse? such as

Log cot B 0.1690 = what angle?

should find the cot first then the log?

your expression makes no sense.

If you mean

log cot B = 0.1690

then that means

cot B = 10^.1690 = 1.4757
B = cot-1 1.4757 = .5955

Finding angles using logarithms can be a bit confusing at first, but with practice, it becomes easier. However, in your explanation, you seem to have made some errors in the calculations.

To find angles using logarithms, you typically need to use a trigonometric identity involving logarithms. For example, the identity log cot θ = log(1/tan θ) = -log tan θ can be used to find an angle given its logarithm.

Let's start with your first example: log cot 0.1690. To find the angle θ, we can use the identity log cot θ = -log tan θ. So, we need to find the logarithm of tan θ that is equal to 0.1690.

To do this, you can take the inverse of the logarithmic function, which is exponentiation. In other words, if log tan θ = 0.1690, then tan θ = 10^0.1690. Using a calculator or a table of logarithms, you can find that 10^0.1690 is approximately 1.4831.

To find the angle θ, you can take the inverse trigonometric function of tan, which is arc tan or atan. So, θ = atan(1.4831). Using a calculator, you can find that θ is approximately 55.238 degrees.

Now let's move on to the second example: log sin (25 degrees 22 minutes). To find the angle θ, we can start by converting the angle into decimal degrees. 25 degrees 22 minutes is equivalent to 25 + 22/60 = 25.3667 degrees.

Next, we need to find the logarithm of sin θ that is equal to log sin (25.3667). Using a calculator or a table of logarithms, you can find that log sin (25.3667) is approximately -1.0770.

To find the angle θ, you can take the inverse of the sine function, which is arcsin or asin. So, θ = asin(10^(-1.0770)). Using a calculator, you can find that θ is approximately 16.231 degrees.

In summary, finding angles using logarithms involves using trigonometric identities and inverse functions. It may seem complicated at first, but as you practice and become familiar with the identities and inverse functions, it becomes easier to solve such problems.