Question

Help
If sin(x) = 1/3 and sec(y) = 25/24
, where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (Enter an exact answer.)

What I know:
cos (y) = 25/24
sin (x + y) = (sinx)(cosy) + (cosx)(siny)
so...
sin (x + y) = (1/3)(24/25) + (cosx)(siny)

How do you get cosx and siny?

Thanks.

Answer 1

u have sin x
use this to get cos x
\(\huge sin^2 x+cos^2x=1\)

Answer 2

similarly u have cos y , find sin y using this :
\(\huge sin^2 y+cos^2y=1\)
can u ?

Answer 3

@franciscanmonk did u understand that ^^ ?

Answer 4

hmm i see. okay ill use it

Answer 5

so... if i use that identity...
i'd get
cosx = sqrt(8/9)
siny = (7/25)

so..
sin(x+y) = (1/3)(24/25) + (sqrt(8/9))(7/25)
sin (x+y) = so...

final answer is
(24-7sqrt(8))/25


right?

Answer 6

sorry.
(24-7sqrt(8))/75

Answer 7

something's wrong.....why minus in between ?

Answer 8

oh sorry its + haha

Answer 9

hmmm...
OH i see. sqrt(8/9) is (2sqrt(2)/3)
(8/25) + (7/25)(2sqrt(2)/3)
(8/25) + (14sqrt(2)/75)
(24/25) + 14sqrtr(2)/75
(24 + 14 sqrt(2))/75)

....right?

Answer 10

thats perfect !

Answer 11

AWESOME!! Thank you!!!!

Answer 12

welcome :)

Answer 13

haha forgot sin^2x + scos^2x = 1