How did they get this???

Question

here's the problem with the solution...
http://www.libraryofmath.com/addition-and-subtraction-formulas.html
It's example (a)...what i do not understand is how did tan 60degrees and tan 45 degrees turn into pie3 and 1???how did they get those 2 numbers?please help?!

Can you please expand on that...I have a test coming up and I just need to know how they got that?

Answer 1

doo not know

Answer 2

Check any trigonometric look up table to find the tangent of 45 degrees is one and tan 60 is sqr(3)

tan = opposite side / near side

An right triangle has one angle of 90 and two of 45 degrees. It will also have two sides of 1 and a hypotenuse of the square root of 2. So by the definition:

tangent 45 = 1 / 1 = 1

Answer 3

you need to understand the trigonemetry identies and trig functions of important angles such as 0, 30, 45, 60 and 90.Google it.

Here's the answer to your problem

degrees = angles
0 0
30 pi/6
45 pi/4
60 pi/3
90 pi/2
that shows how degrees equals angles where pi = 180 degrees


for your question:

Tan(theta) = sin(theta)/cos(theta).
So in the case of tan = 60 degrees,
you have tan60 = sin60/cos60 =( (square root3)/2)/ (1/2)
that equals sqrt(3)/1 = sqrt of 3

Answer 4

tan of 45 degrees is 1 and tan of 60 is the square root of 3 (not pie 3). Either use a calculator or use your unit circle to figure this out on your own if you need to.

Answer 5

All these can be calculated directly from 30-60-90 or 45-45-90 special triangles. This topic is generally covered in Geometry.

Answer 6

its not pie3 and 1

its (3)^.5

aka the square root of 3

and it can be found on tables like this: http://www.analyzemath.com/trigonometry/special_angles_1.gif

or you can draw it...although it is time-consuming

so it makes sense that all the solver did was substitute 3^.5 for tan(60) and the appropriate numbers for the other trigonometric expressions (tan 45=1).

Answer 7

tan 105*=tan(60+45)
=tan60+tan45/1-tan60tan45
value of tan60=rt3
value of tan45=1
substituting
tan 105=rt3+1/1-rt3*
now rationalise the dr to get the answer