Trig

Trig....????
by elson7997

Find the value of the trig function:
tan 64 degrees 6' 45"

Answer(s):

Answer by FIU
The angle is 64 + 6/60 + 45/3600 = 64.1125 degrees
Tan of this is 2.0606

Answer by RAJASEKHAR P
I think every body knows that value for Tan 64-06-45 could be directly obtained from Table by interpolating suitably between Tan 64 & Tan 65

If we view the Question differently, that ,with out tables can we calculate the value of Tan 64-06-45. Then question becomes more interesting.......................................

Let us try

Tan 60 = SQRT(3)= 1.732
Tan (60+2) = (Tan 60 +Tan 2)/(1-Tan60*Tan2)

Tan (A+B) rule applied above

But Tan 2 can be approximated to Sin 2which is again PI*2/180 ( Angle being small - Up to 3.75 All Indian texts right from Aryabhateeyam consider like this.........A better approximation By Madhava discussed in Tantrasangraha & Yuktibhasa)

2 degree to radian 2*PI/180 =

Then Tan 2= 0.0349 (appx)

Then Tan 62 = (1.732 +0.0349)/(1-1.732*0.0349)
=1.7669/0.93955=1.880

Now again Tan 64-06-45 =

Tan 62+Tan (2-06-45)/(1-Tan62*Tan(2-06-45)

Again covert Angle 2-06-45 to radian which will be
2.1125*3.1415/180=0.03687 (appx)
Now Tan (64-06-45) = 1.91687/0.93068=2.0596 (Apprx)

(Actual value- 2.0605)

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