Question

find sinø such that 3cosø+4sinø=4​

Answer 1

Answer:

sin theta = 1 or 7/25

Step-by-step explanation:

i am using A in place of theta

3cosA + 4sinA = 4

3cosA = 4 - 4sinA

3cosA = 4(1 - sinA)

squaring both side

9cos^2A = 16(1 - sinA)^2

9(1 - sin^2A) = 16(1 - sinA)^2

9(1 - sinA)(1 + sinA) - 16 ((1 - sinA)^2 = 0

(1 - sinA) * {9(1+sinA) - 16(1 - sinA)} = 0

this means either

1 - sinA = 0 which gives sinA = 1

or, 9(1+sinA)-16(1-sinA) = 0

9 + 9sinA - 16 + 16sinA = 0

25 sinA = 7

sinA = 7/25