SOLUTION: 1. Find sin B and cos B if tan B is 40/9. 2. Find sin A and tan A if cos A is 3√34/34.

Algebra ->  Trigonometry-basics -> SOLUTION: 1. Find sin B and cos B if tan B is 40/9. 2. Find sin A and tan A if cos A is 3√34/34.       Log On


   

Question 374828: 1. Find sin B and cos B if tan B is 40/9.
2. Find sin A and tan A if cos A is 3√34/34.

Found 2 solutions by vasumathi, Fombitz:
Answer by vasumathi(46) About Me  (Show Source):
You can put this solution on YOUR website!
1. Find sin B and cos B if tan B is 40/9
Solution: tan B = 40/9
so opposite side = 40
and adjacent side = 9
we can calculate the hypotenuse as follows...
hypotenuse = sqrt(40^2+9^2) = sqrt(1600 + 81) = sqrt(1681)= 41
sin B = opposite side/hypotenuse = 40/41
cosB = adjacent side/ hypotenuse= 9/41
2. Find sin A and tan A if cos A is 3√34/34.
Solution: cos A = 3sqrt(34)/34
sin^2A + cos^2A = 1
sin^2(A) +9*34/34^2
sin^2(A) + 306/1156=1
sin^2(A) = 1-306/1156= 850/1156=25*34/34*34
sin(A) = 5 sqrt 34/34
tan A = sin A / cosA= (5 sqrt 34/34)/(3 sqrt(34)/34)= 5/3

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28B%29=40%2F9
.
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tan%28B%29=sin%28B%29%2Fcos%28B%29
sin%28B%29=40%2FH
cos%28B%29=9%2FH
.
.
%28sin%28B%29%29%5E2%2B%28cos%28B%29%29%5E2=1
%2840%2FH%29%5E2%2B%289%2FH%5E2%29=1
1600%2FH%5E2%2B81%2FH%5E2=1
1681%2FH%5E2=1
H%5E2=1681
H=sqrt%281681%29
H=41
So then,
sin%28B%29=40%2F41
cos%28B%29=9%2F41
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%28sin%28A%29%29%5E2%2B%28cos%28A%29%29%5E2=1
%28sin%28A%29%29%5E2%2B%28%289%2834%29%29%2F%2834%29%5E2%29=1
%28sin%28A%29%29%5E2%2B%289%2F34%29=1
%28sin%28A%29%29%5E2=34%2F34-9%2F34
%28sin%28A%29%29%5E2=25%2F34
sin%28A%29=5%2Fsqrt%2834%29
sin%28A%29=%285%2Asqrt%2834%29%29%2F34
.
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tan%28A%29=sin%28A%29%2Fcos%28A%29
tan%28A%29=5%2F3