Expert: Paul Klarreich - 1/8/2008

Question
find the value of sin(alpha + theta) if sin alpha= 3/5, cos theta= 12/13, 0 degrees < alpha < 90 degrees, and 0 degrees < theta < 90 degrees

a) 56/65
b) 16/65
c) 63/65
d) 33/65

Answer
Questioner:   arlene
Category:  Calculus
Private:  No
 
Subject:  analysis of functions
Question:  find the value of sin(alpha + theta) if sin alpha= 3/5, cos theta= 12/13, 0 degrees < alpha < 90 degrees, and 0 degrees < theta < 90 degrees

a) 56/65
b) 16/65
c) 63/65
d) 33/65

....................................
Hi, Arlene,

Use: sin(a + t) = sin a cos t + cos a sin t.

Now sin a is given as 3/5.  Make a nice right triangle with hypot = 5, opp leg = 3.  Then the other leg = 4 and cos a = 4/5.

Now cos t is given as 12/13.  Make a nice right triangle with hypot = 13, adj leg = 12.  Then the other leg = 5 and sin t = 5/13.

Ready to go:

sin(a + t) = sin a cos t + cos a sin t.
sin(a + t) = (3/5)(12/13) + (4/5)(5/13)
sin(a + t) = 36/65 + 20/65 = 56/65