If cos b=3/5 and sin a=4/5, where a and b are between 0 and pi/2, evaluate the following:

Question

If cos b=3/5 and sin a=4/5, where a and b are between 0 and pi/2, evaluate the following:

 

a) Sin2a

 

b)cos(a-b)

Answer 1

Hi Paula,

 

cos(b) = 3/5 means angle be is one of the angles of a very familiar triangle whose sides are 3, 4, and 5; with 5 being the hypotenuse. Angle a is actually is equal to angle a (if you draw the right triangle and properly label it you can easily see that that is the case) 

Thus, cos(a-b) = cos (a - a) = cos(0) = 1     //a = b

Sin(2a)? you may have to go to periodic table for that (or your calculator. The number you get, if you did it right, is not any one of the special triangles 

 

Use calculator to find:
arcsin (4/5) arcos (3/5) = 52.13 deg 

Answer 2

Hi Paula,

 

If cos b=3/5 and sin a=4/5, then sinb = 4/5 and cosa = 3/5

 

a) sin2a = 2sinacosa

= 2*4/5*3/5

= 24/25

 

b) cos(a - b) = cosacosb + sinasinb

= 3/5*3/5 + 4/5*4/5

= 9/25 + 16/25

= 25/25

= 1