SOLUTION: What are the values of cos α and tan α, if: sin a = 40/41 sin a = 3/5 sin a = 0.8

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Question 1098456: What are the values of cos α and tan α, if:

sin a = 40/41
sin a = 3/5
sin a = 0.8
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sin^2a+cos^2a=1
also 9-40-41 is a right triangle (81+1600=1681), just like 3-4-5
Therefore, cos a is 9/41 for the first
tangent is sin/cos, so tan a is 40/9
and cos a is 0.6 because 0.6^2=0.36 and sin a=0.8 means sin ^2 a is 0.64, and 0.64+0.36=1

Answer by ikleyn(52765) About Me  (Show Source):
You can put this solution on YOUR website!
.
What are the values of cos(a) and tan(a), if:
~~~~~~~~~~~~~~~~~~~

    1.  Notice that I edited your writing (!)

    2.  Since the ondition doesn't say to which quadrant the angle "a" does belong, I will assume it lies in QI.

Solution 

sin a = 40/41  

    ====>  cos(a) = sqrt%281-sin%5E2%28a%29%29 = sqrt%281-%2840%2F41%29%5E2%29 = sqrt%281-1600%2F1681%29 = sqrt%2881%2F1681%29 = 9%2F41;

           tan(a) = sin%28a%29%2Fcos%28a%29 = %28%2840%2F41%29%29%2F%28%289%2F41%29%29 = 40%2F9.


sin a = 3/5

    ====>  cos(a) = sqrt%281-sin%5E2%28a%29%29 = sqrt%281-%283%2F5%29%5E2%29 = sqrt%281-9%2F25%29 = sqrt%2816%2F25%29 = 4%2F5;

           tan(a) = sin%28a%29%2Fcos%28a%29 = %28%283%2F5%29%29%2F%28%284%2F5%29%29 = 3%2F4.


sin a = 0.8   Do it on your own using my template above.
              It will be good exercise to you.


Notices: 
    1.  In problems like this the condition usually says to which quadrant the angle "a" does belong.  Without it, the unique answer is impossible.

         OK, I assume that you don't know it.  //Or do not think about it . . . 


    2.  You write and denote alpha and "a" as identical quantities without saying it.


    3.  So be careful: your writing tells a lot about you: you even may do not know WHAT it tells.