Question
Asked Oct 13, 2019
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12
with A in QII and sin B = -
13
15
with B in QIII. Find sin(A + B), cos(A + B), and tan(A + B)
17
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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12 with A in QII and sin B = - 13 15 with B in QIII. Find sin(A + B), cos(A + B), and tan(A + B) 17 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

Refer to the question, we have to find the value of sin(A+B) , cos(A+B) and tan(A+B) when provided with sin A=12/13 with A in Q2 and Sin B=-15/17 with B in Q3.

12
sin A A is in quadrant 2
13
15
Bis in quadrant 3
17
sin B
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12 sin A A is in quadrant 2 13 15 Bis in quadrant 3 17 sin B

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Step 2

Now use the formula for the identity  sin (A+B), cos (A+B) and tan(A+B).

B
sin Acos A +sin Bcos B
sin (A
cos (A B) cos A cos B - sin A sin B
tan Atan B
tan (A B)
1-tan A tan B
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B sin Acos A +sin Bcos B sin (A cos (A B) cos A cos B - sin A sin B tan Atan B tan (A B) 1-tan A tan B

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Step 3

Now as we know that in first quadrant all the trigonometric ratios are positive , in second only sine and cosec is positive rest are negative, in thir...

12 P
sin A
., A is in quacrant 2
13 H
Base = H2-P
= v133 -12
Base 5
5
cos A =
13
12
tan A
5
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12 P sin A ., A is in quacrant 2 13 H Base = H2-P = v133 -12 Base 5 5 cos A = 13 12 tan A 5

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Tagged in

Math

Trigonometry

Trigonometric Ratios