College level trig: what is the 30' part of Tan 62 degrees 30' ?

acm123

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Okay so this is probably a real simple thing but my professor didn't go over any examples like this.
Any way on my homework it asks me to find:

Tan 62 degrees 30'

Finding tan(62) is easy I mea I just punch it in my calculator, but what in the world is the 30 suppose to be and what do I have to do with it?

I know the answer is 1.921 (rounded 4 decimal places) but I don't know what steps were done to do that.

The second part of the question is to find:

Cot 27 degrees 30'
I know Cot is 1/tan (theta) which is basically cos theta/sin theta, but again I have no idea what the 30 is and what I do with it.

Again this is probably really simple thing but I couldn't even find example problems that looked like this.
 
Okay so this is probably a real simple thing but my professor didn't go over any examples like this.
Any way on my homework it asks me to find:

Tan 62 degrees 30'

Finding tan(62) is easy I mea I just punch it in my calculator, but what in the world is the 30 suppose to be and what do I have to do with it?

I know the answer is 1.921 (rounded 4 decimal places) but I don't know what steps were done to do that.

The second part of the question is to find:

Cot 27 degrees 30'
I know Cot is 1/tan (theta) which is basically cos theta/sin theta, but again I have no idea what the 30 is and what I do with it.

Again this is probably really simple thing but I couldn't even find example problems that looked like this.

1° = 60' ← read as 1 degree = 60 minutes
 
...find: Tan(62 degrees 30')

Finding tan(62) is easy I mea I just punch it in my calculator, but what in the world is the 30 suppose to be and what do I have to do with it?
Ouch! They were supposed to cover "degrees-minutes-seconds" in class before assigning homework on it! To make up for this breech, try studying some lessons online, such as here.

Once you have studied at least two lessons from the list, please attempt the exercise. If you still get stuck, you can then reply with a clear listing of your efforts, starting with your conversion of "thirty minutes" to a decimal portion of a degree. (Hint: Divide.) ;)
 
Quick explanation:

30'

The apostrophe symbol indicates "minutes".

A minute is a fractional part of a degree.

1 minute = 1/60th of a degree

Hence, 30' = 30/60ths of a degree (i.e., 0.5 degrees)

30"

The quote symbol indicates "seconds".

A second is a fractional part of a minute (thus, also, a fractional part of a degree).

1 second = 1/60th of a minute

1 second = 1/3600th of a degree

Hence, 30" = 30/3600ths of a degree (i.e., 0.0083 degrees, rounded)

1° 30' 30"

1° + 30/60° + 30/3600° = 1.5083° (rounded)

Please follow stapel's advice, and work through some lessons and examples. :cool:
 
COT 57 degrees 30 minutes?

Ouch! They were supposed to cover "degrees-minutes-seconds" in class before assigning homework on it! To make up for this breech, try studying some lessons online, such as here.

Once you have studied at least two lessons from the list, please attempt the exercise. If you still get stuck, you can then reply with a clear listing of your efforts, starting with your conversion of "thirty minutes" to a decimal portion of a degree. (Hint: Divide.) ;)


Hi:
I was able to figure out Tan(32)30' by;
32+30(1/60) which gave me 32.5.

However I'm still having trouble with Cot(57)30', I know that COT is the reciprocal of tan, but for my hw (its online) I don't have the option to input a fraction. So I converted 57degrees 30' and got 57.5 but that was wrong, so I'm not really sure what to do.
 
Hi:
I was able to figure out Tan(32)30' by;
32+30(1/60) which gave me 32.5.

However I'm still having trouble with Cot(57)30', I know that COT is the reciprocal of tan, but for my hw (its online) I don't have the option to input a fraction. So I converted 57degrees 30' and got 57.5 but that was wrong, so I'm not really sure what to do.
What did you get for cot(57.5) in your calculator?

You probably calculated tan instead of cot!
 
I was able to figure out Tan(32)30' by;
32+30(1/60) which gave me 32.5.
...and then you took the tangent of this value, right?

However I'm still having trouble with Cot(57)30', I ...converted 57degrees 30' and got 57.5 but that was wrong...
No; this is correct. Fifty-seven degrees and thirty minutes is indeed equal to 57.5 degrees.

so I'm not really sure what to do.
Now that you have the angle measure in decimal degrees, you need to plug this into the cotangent function (or else the tangent function, and take the reciprocal). ;)
 
COT 57 degrees 30 minutes

What did you get for cot(57.5) in your calculator?

You probably calculated tan instead of cot!

I just conveted like I did for tan which was wrong, I ended up having to do another problem which was;
a) Tan (68)30'
b)Cot(21)30'

both equaled 2.5836 which I got by converting. I guessed for part b, but I didn't get why they were the same?
 
I just converted like I did for tan which was wrong …
I think Subhotosh was asking you for your numerical result; we don't know what you did.

Tan(68)30'

Cot(21)30'

both equaled 2.5836 … I [don't] get why they [are] the same?
They have the same value because of symmetry:

21.5° is 21.5 units to the right of 0°

68.5° is 21.5 units to the left of 90°.

In other words:

cos(68.5°) = sin(21.5°)

AND

sin(68.5°) = cos(21.5°)

Therefore:

tan(68.5°) = sin(68.5°)/cos(68.5°) = cos(21.5°)/sin(21.5°) = cot(21.5°)
 

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