Question 633159: how do i calculate these angles?
cos^-1(4/5)
csc(theta)=7/3
tan36(degrees)
cot12(degrees)24"
sin158.9(degrees)
sec(theta)=1.2345
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Your will need a calculator (or calculator program) for this, Make sure it is working in degree mode. (Try tan(45). If you get a 1 from the calculator, then you are in degree mode. If you get something else you will need to set your calculator to degree mode before you try any of the following.)
For the 1st, 3rd and 5th ones, just enter what you see into the calculator.
For the 2nd and 6th ones, you will have to find reciprocals since there is no csc or sec buttons on the calculator. The reciprocal of csc is sin. So if the csc(theta) is 7/3 then the sin(theta) = 3/7. Then to find theta you use sin^-1(3/7). For the 6th one, use the fact that sec and cos are reciprocal functions. So it sec(theta) = 1.2345 then cos(theta) = 1/1.2345. Then use cos^-1(1/1.2345) to find theta.
For the cot, first we need to change the angle measure to a decimal number of degrees. Is that actually 24" in the problem? 24" means 24 seconds. 24' means minutes. I'm going to guess that it should be 24 minutes (24'). To convert his to degrees you divide by 60: 24/60 = 2/5 = 0.4. (If it is really 24 seconds (24"), then use 24/(60*60) = 0.00666667). Then add the decimal to 2 to get the full angle: 2.4 (or 2.00666667). Next, since your calculator does not have a cot button we must use the reciprocal function, tan. So find tan(2.4) (or tan(2.00666667) and then find its reciprocal. (Many calculators have a "1/x" button to find reciprocals. If not, then just use 1/tan(2.4) (or 1/tan(2.00666667)
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