Question
Asked Oct 20, 2019
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15
with A in QIII and sin B -
17
with B in QIII. Find sin(A B), cos(A + B), and tan(A B)
13
Let sin A
sin(AB)
cos(AB)=
tan(AB)
In what quadrant does A + B terminate?
quadrant I
quadrant II
quadrant III
quadrant IV
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15 with A in QIII and sin B - 17 with B in QIII. Find sin(A B), cos(A + B), and tan(A B) 13 Let sin A sin(AB) cos(AB)= tan(AB) In what quadrant does A + B terminate? quadrant I quadrant II quadrant III quadrant IV

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Expert Answer

Step 1

sinA=15/17 and A is in quadrant II

There cosA will be negative.

CosA= -8/17

COSA=-1- sin A
15
COSA=
17
225
1-.
289
COSA=
64
COSA=-
289
cosA=-
17
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COSA=-1- sin A 15 COSA= 17 225 1-. 289 COSA= 64 COSA=- 289 cosA=- 17

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Step 2

sinB= -5/13 and B is in quadrant III

There cos is negative too 

cosB= -12/13

cosB-1- sin B
2
5
cosB=-
13
25
1-
169
COSB=
144
cosB=
169
12
13
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cosB-1- sin B 2 5 cosB=- 13 25 1- 169 COSB= 144 cosB= 169 12 13

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Step 3

Use the formula sin(A+B)=sinAcosB+cosAsin...

sin(A+B)
=sinAcosB+cosAsinB
15
-12
-8
17
13
17
13
-180
40
221
221
-140
221
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sin(A+B) =sinAcosB+cosAsinB 15 -12 -8 17 13 17 13 -180 40 221 221 -140 221

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