Question

Який знак має: 1)sin186* 2)tg104* 3)ctg340* 4)cos(-78*) 5)ctg(-291*) 6)sin3π/7*. 7)tg9π\8. 8)cos(-13π/12)?

Answer 1

1) -0.60202393755 ; 2) 0.33966973169 ; 3) 1.16816202331 ; 4)-0.85780309324 ; 5) 0.42595533088 ; 6) 0.97492791218 ; 7) 0.06176338482; 8) 0.9982363151.  

Answer 2

1. sin 186° has a negative value, because 186° is in the third quadrant where sine is negative. Using the identity sin(180° + x) = -sin(x), we can write:

sin 186° = sin (180° + 6°) = -sin 6°

2. tg 104° has a positive value, because 104° is in the second quadrant where tangent is positive. Using the identity tg(x + 180°) = tg(x), we can write:

tg 104° = tg (104° - 180°) = tg (-76°)

3. ctg 340° has a positive value, because 340° is in the fourth quadrant where cotangent is positive. Using the identity ctg(x + 180°) = ctg(x), we can write:

ctg 340° = ctg (340° - 180°) = ctg 160°

4. cos(-78°) has a positive value, because -78° is in the second quadrant where cosine is positive. Using the identity cos(-x) = cos(x), we can write:

cos(-78°) = cos(78°)

5. ctg(-291°) has a negative value, because -291° is in the third quadrant where cotangent is negative. Using the identity ctg(x + 180°) = ctg(x), we can write:

ctg(-291°) = ctg(-291° + 180°) = ctg(-111°)

6. sin(3π/7) has a positive value, because 3π/7 is in the first quadrant where sine is positive.

7. tg(9π/8) has a negative value, because 9π/8 is in the third quadrant where tangent is negative. Using the identity tg(x + π) = tg(x), we can write:

tg(9π/8) = tg(9π/8 - π) = tg(π/8)

8. cos(-13π/12) has a negative value, because -13π/12 is in the third quadrant where cosine is negative. Using the identity cos(-x) = cos(x), we can write:

cos(-13π/12) = cos(13π/12)