sin theta+cos theta=7/5
and sin theta×cos theta=12/25
find sin theta and cos theta
Answers
Step-by-step explanation:
given sin theta+cos theta=7/5->EQ1
sin theta×cos theta=12/25->EQ2
to find sin theta and cos theta
LET cos theta=7/5-sin theta->EQ3
and EQ3 IN EQ2
THERFORE sin theta(7/5-sin theta)=12/25
-sin^2 theta+7/5sin theta-12/15=0
we can written as
sin^2 theta-7/5sin theta+12/15=0
it is in the form of ax^2+bx+c=0
so using formula (-b+-root of (b^2-4ac))/2a
here a=1,b= -7/5,c=12/25
substituting in formula
(-(-7/5)+-root of (-7/5^2-4(1)(12/25)))/2(1)
(7/5+-root of (49/25-48/100))/2
( 7/5+-root of (1.48))/2
7/5+-1.216/2->7/5+1.216/2(or)7/5-1.216/2
1.3082762531 (or)0.092
let substitute eq 1 first value
1.3082762531 +cos theta=7/5
cos theta=0.092
approximately cos theta =0.092
sin theta =1.3082762531
thank you very much
the problem
it not matching with eq 2