Question

Given that tanx=12/5, cosy =-3/5 and that the angles x and y are in the same quadrqnt; calculate without use of tables, the value of 1) sin(x+y), 2)cos(y+2)​

Answer 1

Given info : tanx = 12/5 and cosy = -3/5 and angles x and y are in the same quadrant.

To find : the value of (1) sin(x + y) (2) cos(x + y) without using tables.

solution : tanx = 12/5 and cosy = -3/5

tan is positive but cosine is negative, it is possible only when x and y are located in 3rd quadrant.

so, tanx = 12/5 ⇒sinx = -12/13,cosx = -5/13

[in 3rd quadrant, sine and cosine are negative]

cosy = -3/5 ⇒siny = -4/5

now sin(x + y) = sinx cosy + cosx siny

= (-12/13) (-3/5) + (-5/13) (-4/5)

= 35/65 + 20/65

= 55/65

= 11/13

therefore the value of sin(x + y) is 11/13

cos(x + y) = cosx cosy - sinx siny

= (-5/13) (-3/5) - (-12/13) (-4/5)

= 15/65 - 48/65

= -33/65

Therefore the value of cos(x + y) = -33/65