i need help /trigonometry?

Question

1. Find the value of:

a. log sin 62° 22’ 33”
b. log cot 28° 13’ 17”
c. log cos 125° 15’ 23”
d. log tan 78° 45’ 50”

Answer 1

First, you must make sure that your calculator is set for DMS mode. If yo don't have DMS mode or don't know how to get to it, you'll have to imput as fractions, for example,
62 degrees 22 min 33 sec = 62 + (22/60) + (33/3600)

Next, you will imput each of these values, find the appropriate trig fuction, and finally take the log of each values. Since no base of the log is specified, log base 10 is assumed. Also, all values are approximate, as they are irrational numbers.
Here we go...
a) -.052562314
b) .270287805 (if your calculator doesn't do cotangents you will have to find the tangent and then do (1/x) for cotangent and then take the log of this result.
c) This one will be a problem since the cosine in the second quadrant is negative and logs are defined only for positive numbers. Anyhow...
log |cos 125*15'23"| = -.238646405
d) .701888735

Answer 2

I don't know where you would use this but...I would convert the degrees, minutes and seconds to decimal degrees first and then just punch the numbers in the calculator.

a) 62deg22'33" = 62 + 22/60+ 33/(60^2) = 62.3758333...

THen evaluate the sine of this angle and then the log of it to get:
-0.052562

b) THe angle = 28 + 13/60 + 17/(60)^2 = 2802213888...
Then do the cot and the log to get" 0.270878

Similarly for the other two

I put a link for a converting explanation below

Answer 3

Depends what sort of calculator you are using. I think all of them now use algebraic logic and have a button to enter angles in degrees, minutes and seconds. I'll refer to this button as D. And make sure your calculator is set to degrees (not radians or grads). It should show "deg", or in some cases just "d" right at the top of the screen.

For the first one, you can key in
sin 62D 22D 33 =
and it should come up with the value of sin 62° 22’ 33” = 0.886008087

Then press
log =
if it's the base 10 log that's required, or press
ln =
if it's the natural log that's required.

Do b. c. and d. the same way.

Answer 4

For the first one, you can key in
sin 62D 22D 33 =
and it should come up with the value of sin 62° 22’ 33” = 0.886008087

Then press
log =
if it's the base 10 log that's required, or press
ln =
if it's the natural log that's required.

Do b. c. and d. the same way.


I was the first one to answer i just had to edit my answer because i spelled somethings wrong

Answer 5

1a. log(sin(62° 22’ 33”))

You want to start from the inside and work your way out.

First, we'll convert 62° 22’ 33” into degrees only (since scientific calculators cannot deal directly with minutes and seconds).

Recall that there are 60 seconds (") in a minute (') and 60 minutes (') in a degree (°).

Let's use dimensional analysis to do the conversion.

33 seconds
= 33 seconds * (1 minutes/60 seconds)
= 0.5500 minutes

22 minutes and 33 seconds
= 22.5500 minutes
= 22.5500 minutes * (1 degree/60 minutes)
= 0.3758 degrees

62 degrees, 22 minutes and 33 seconds
= 62.3758 degrees

Now, make sure your calculator is set in "degree mode".

sin(62.3758) = 0.8660

Finally, you would take the logarithm of this number. I will assume that you mean the log is base 10.

log(0.866) = -0.0526

Thus, log(sin(62° 22’ 33”)) = -0.0526

Parts b, c, and d should be treated similarly.

For parts b and d, it may be useful to recall:
cot(x) = cos(x)/sin(x)
tan(x) = sin(x)/cos(x)