SOLUTION: Find the exact value of the following under the given conditions.
if tan(x)= -4/3
and (pi/2)< x < pi
and
if sin(y)= 2/3
and 0< y < (pi/2)
find tan(x+y)
show wor
Algebra.Com
Question 965366: Find the exact value of the following under the given conditions.
if tan(x)= -4/3
and (pi/2)< x < pi
and
if sin(y)= 2/3
and 0< y < (pi/2)
find tan(x+y)
show work and state exact value
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact value of the following under the given conditions.
if tan(x)= -4/3
and (pi/2)< x < pi
and
if sin(y)= 2/3
and 0< y < (pi/2)
find tan(x+y)
***
tanx=-4/3 ((3-4-5) reference right triangle in quadrant II)
sinx=4/5
cosx=-3/5
..
siny=2/3
cosy=
..
sin(x+y)=sinx*cosy+cosx*siny=4/5*√5/3+-3/5*2/3=4√5/15-6/15=(4√5-6)/15
cos(x+y)=cosx*cosy-sinx*siny=-3/5*√5/3-4/5*2/3=-3√5/15-8/15=-(3√5+8)/15
tan(x+y)=sin(x+y)/cos(x+y)=-(4√5-6)/(3√5+8)
..
check:
tanx=-4/3 (Q2)
x=126.87˚
siny=2/3 (Q1)
y=41.81˚
x+y=168.68
tan(x+y)=tan(168.68)≈-0.2002
exact value as computed above=-(4√5-6)/(3√5+8)≈-0.2002
RELATED QUESTIONS
find the exact value given the following conditions
a. cos (a + b)
b. sin (a + b)
c. (answered by lwsshak3)
Find the exact value if 0 < x < pi/2 and 0 < y < pi/2 ; sin(x+y) if sin(x) = 3/5 and... (answered by fractalier)
Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and... (answered by lwsshak3)
Find the exact value under the given conditions.
cos a = 1/3 , 0 < a < pi/2. sin b=... (answered by lwsshak3)
what is the exact value if 0 < x < pi/2 and 0 < y < pi/2, of the cos (x+y) if the tan x = (answered by lwsshak3)
If {{{tan(3x) tan (2x) = tan (pi/4)}}}, find the value of {{{sin(5x)}}}, given that {{{0... (answered by ikleyn)
if sin x=3/5,pi/2 < x < pi, then find the value of cos x,tan x,sec x and cot... (answered by ikleyn)
Find the exact value of each of the following under the given conditions:
{{{cotA=... (answered by lwsshak3)
sin(x)=8/17 and pi/2 less than x less than pi. Find the exact value of... (answered by stanbon)