Find the exact value of sin(a+b): If sina=3/5, 0< a< pi/2; cos B= 2 root 5/5, =pi/2

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Find the exact value of sin(a+b): If sina=3/5, 0< a< pi/2; cos B= 2 root 5/5, =pi/2

Mathematics
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hmm.. sin ( a+ b) = sina cosb + sinb cosa We are given: sina = 3/5 , cos b = 2 root 5/5 So draw out two triangles: |dw:1433425889828:dw|
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sin (a + b ) = sina cosb + sinb cosa We know sina 3/5 , cosb = 2sqrt5/5 So find sinb and cosa from the triangles and then plug it into the formula in the first line :)
what don't you understand?
how do you find sinb amd cos a?
look at the triangles. Sin = opposite/ hypotenuse Cos = adjacent/ hypotenuse |dw:1433427282198:dw|
ok so how did you get those Triangles in the beginning?
sin = opposite / hypotenuse right? They told us that "Sina = 3/5" This means opposite side = 3 and hypotenuse = 5 Therefore you set up the right angled triangle and draw it out.. Same with cosb = 2sqrt 5/5 cos = adjacent / hypotenuse Therefore adjacent = 2sqrt 5 , hypotenuse = 5 Then draw out the right angled triangle and label the sides.

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