SOLUTION: Suppose sin x = 1/7
cos x > 0, sin y = −2/5
and cos y < 0. Then
cos x =
cos y =
Find each of the following quantities:
sin(x + y) =
cos(x + y) =
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Question 923447: Suppose sin x = 1/7
cos x > 0, sin y = −2/5
and cos y < 0. Then
cos x =
cos y =
Find each of the following quantities:
sin(x + y) =
cos(x + y) =
tan(x + y)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Suppose sin x = 1/7
cos x > 0, sin y = −2/5
and cos y < 0. Then
cos x =
cos y =
Find each of the following quantities:
sin(x + y) =
cos(x + y) =
tan(x + y)
***
reference angle x is in quadrant I where sin>0, cos>0
sinx=1/7
cosx=√(1-sin^2x)=√(1-1/49)=√(48/49)=√48/7)
..
reference angle y is in quadrant III where sin<0, cos<0
siny=-2/5
cosy=-√(1-sin^2y)=-√(1-4/25)=-√(21/25)=-√21/5
..
sin(x+y)=sinxcosy+cosxsiny=1/7*-√21/5+√48/7*-2/5=-√21/35-2√48/35=-(√21+2√48)/35
cos(x+y)=cosxcosy-sinxsiny=√48/7*-√21/5-1/7*-2/5=-√1008/35+2/35=(-√1008+2)/35
tan(x+2)=sin(x+2)/cos(x+2)=-(√21+2√48)/(-√1008+2)
check:
sinx=1/7
x≈8.21˚
siny=-2/5
y≈203.58˚
x+y≈203.58+8.21≈211.79
..
sin(x+y)≈sin(211.79)≈-0.5268 (w/calculator)
exact value as computed=-(√21+2√48)/35≈-0.5268
..
cos(x+y)≈cos(211.79)≈-0.8500 (w/calculator)
exact value as computed=(-√1008+2)/35≈-0.8500
..
tan(x+y)=tan(211.79)≈0.6198 (w/calculator)
exact value as computed=-(√21+2√48)/(-√1008+2)≈.5268/.8500≈0.6198
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