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Trig Functions of Angles Expressed in Degrees and Minutes

Date: 05/04/98 at 19:15:06
From: Reddog
Subject: Trigonometry

I'm a student of a technical college. We just started using trig for 
machining applications. I'm having trouble, due to my schedule not 
allowing me to attend lectures. I'm having trouble with cotangent, 
secant, and cosecant functions with my calculator. I'm using a Casio 
fx-250HC fraction calculator. Also, would help me prove my answers so 
I can double-check myself? Below are some sample problems.

Find the value of the following:

   1) Sin 75deg, 11min
   2) Cot 19deg, 14min                   
   3) Sec 44deg, 44min                    
   4) Cosec 89deg, 41min

Find the angle (in degrees and minutes):

   1) Sin .69587
   2) Cos .35501
   3) Tan .76915
   4) Cot .24200
   5) Sec 1.3412
   6) Cosec 68.700
   7) Sin .84870

Date: 05/04/98 at 20:37:33
From: Doctor Jaffee
Subject: Re: Trigonometry

Hi Reddog,

I'm not familiar with the calculator you are using, but I think I can 
help you out with some general solutions.

First of all, I noticed that all of the questions you presented were 
in terms of degrees. Before you get started, make sure that your 
calculator is in the degree mode (and not radian or gradient mode).

Second, most scientific calculators do trigonometry calculations by 
receiving the number first, then the function. For example, if you 
want to know the sin of 30 degrees, enter 30, then hit the "sin" 
button. The result should be 0.5. If your calculator works like most 
graphing calculators, then you would enter sin first, followed by 30.

Since, you're asking specifically about secant, cosecant, and 
cotangent, I'll assume that you've figured that out already.

Now, let's consider sin 75 deg, 11 minutes. Some calculators have a 
button that allows you to enter minutes and seconds. If yours doesn't, 
you can use the fact that there are 60 minutes in a degree, so you can 
convert the problem to sin 75 11/60 degrees. You can solve any problem 
involving sine, cosine, or tangent this way.

To find cot 19 deg 14 minutes, find tan 19 deg 14 minutes. Since the 
cotangent and tangent function are reciprocals of each other, use the 
"1/x" button (or maybe it says x^(-1)) to the tangent, and you will 
get the cotangent. Similarly, the secant is the reciprocal of the 
cosine, and the cosecant is the reciprocal of the sine.

Now, for the last seven problems, I assume that what you are asking is 
something like "Sin of what equals .69587?" To answer this type of 
problem, you want to use the "2nd" function button (it might say 
"shift" or "INV" on your calculator). In any case, enter .69587, then 
the "2nd" function button, then the "sin" button. I get 44.097 degrees 
on my calculator. But .097 x 60 = 6, approximately; so, my final 
answer is 44 degrees and 6 minutes.

If the secant of something equals 68.7, then the cosine of something 
equals 1/(68.7). Therefore, the unknown number can be found by 
entering 1/(68.7), then "2nd" function, then "cos."

Well, I hope this explanation has been helpful. Good luck in 
your course.

-Doctor Jaffee, The Math Forum
Check out our web site!   

Date: 05/04/98 at 23:25:26
From: Wayne Retzack
Subject: Re: Trigonometry

Thanks, Doc!
Associated Topics:
High School Calculators, Computers
High School Trigonometry

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