Question

Si sen =−7/25 y cos⁡= −4/5, determine:
sen (α+β)=

Answer 1

Answer:

sin(α+β)= 12/25

Step-by-step explanation:

sinα= -7/25

cosβ= -4/5

sin(α+β)= sinα cosβ + cosα sinβ

by Pythagoras theorem

adj= √(hypo)^2-(opp)^2

sinα=-7/25

cosα= 24/25

by Pythagoras theorem

adj= √(hypo)^2-(opp)^2

cosβ= -4/5

sinβ= 3/5

sin(α+β)= sinα cosβ + cosα sinβ

= (-7/25 ) (-4/5) + (24/25) (3/5)

= -27/25+ 39/25

= 12/25

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Answer 2

Given :- sin A = (-7/25) , cos B = (-4/5) ,

To Find :-

• sin (A + B) = ?

Answer :-

→ sin A = (-7/25) = P/H

so, using pythagoras theorem,

→ B = √(H² - P²) = √(625 - 49) = √576 = 24

then,

→ cos A = B/H = (-24/25)

similarly,

→ cos B = (-4/5) = B/H

so,

→ P = √(5² - 4²) = 3

then,

→ sin B = P/H = (-3/5)

now,

→ sin(A + B) = sinA * cosB + cosA * sinB

→ sin(A + B) = (-7/25) * (-4/5) + (-24/25) * (-3/5)

→ sin(A + B) = (28/125) + (72/125)

→ sin(A + B) = (100/125)

→ sin(A + B) = (4/5) (Ans.)

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