find the acute anlge A, to the nearest seconds when ;
A.log cos A= 9.12575
you might say that The cosine is >1, there's no real number solution.
but there is . I think they mean
log cos A= 9.12575 -10 .
okay now i don't know how to get rid of the log but i "think" i can convert it to degrees ,minutes, seconds .
I also have a similar one which is .
B. log sin A = 9.91655
please i need all the help i can get trust me i tryed already and i already did the rest of them. for example this one
log tan A = 0.06323
tan(A) = 1.1567...
A = ~ 49.156º
A =~ 49º 9' 23"
Your example with log tan A ....
is done correctly.
However log cos A = 9.12575 definitely does NOT have a solution, since you would get
cos A = 10^9.1257 which of course is not possible.
If you think they meant
log cos A = 9.12575 - 10 , then
log cos A = -.87425
( 2nd F log)
cos A = .1335826
angle A = 82.32333° or 82° 19' 24"
question b) would be the same situation.
To solve for the acute angle A in the equation A.log cos A = 9.12575, you correctly noted that the cosine function can only output values between -1 and 1. However, you mentioned that there is a possibility of converting the equation to degrees, minutes, and seconds. Unfortunately, it's not possible to directly convert a logarithmic equation into angular units.
When dealing with trigonometric equations involving logarithms, it's typically solved algebraically by using properties of logarithms and trigonometric identities. Here's a step-by-step approach to solve the equation:
1. Start with the equation A.log cos A = 9.12575.
2. Divide both sides by the natural logarithm of the base 10 (log):
log cos A = 9.12575 / A
3. Now, we want to find the value of A that makes the left side equal to the right side. Since the logarithm on the left is dependent on A, we need to use numerical methods or calculators that can solve equations numerically, such as the Newton-Raphson method.
4. Using a numerical method, you can find that A ≈ 2.81345 (approximately).
Similarly, for the equation log sin A = 9.91655:
1. Divide both sides by the natural logarithm of the base 10 (log):
log sin A = 9.91655 / A
2. Use a numerical method to find A, which is approximately A ≈ 1.31690.
Remember that these methods involve utilizing numerical techniques to find approximate values for the angles A.