To find the value of sin(-810°), we must first find the equivalent angle between 0° and 360°.
-810° + 360° = -450°
sin(-450°) = sin(360° - 450°) = sin(-90°) = -sin(90°) = -1
Next, we will find the value of cos(900°). Since cos(900°) = cos(900° - 360°) = cos(540°) = cos(180°) = -1.
Finally, to find ctg(675°), we use the relationship between cotangent and tangent:ctg(675°) = 1/tan(675°) = 1/tan(675° - 360°) = 1/tan(315°)
In the fourth quadrant, the tangent function is positive, so we find the reference angle for 315°:315° - 270° = 45°
This means that tan(315°) = tan(45°) = 1, and therefore ctg(675°) = 1.
Putting it all together:-810° + cos 900° - ctg 675° = -1 + (-1) - 1 = -3
Therefore, the final answer is -3.
To find the value of sin(-810°), we must first find the equivalent angle between 0° and 360°.
-810° + 360° = -450°
sin(-450°) = sin(360° - 450°) = sin(-90°) = -sin(90°) = -1
Next, we will find the value of cos(900°). Since cos(900°) = cos(900° - 360°) = cos(540°) = cos(180°) = -1.
Finally, to find ctg(675°), we use the relationship between cotangent and tangent:
ctg(675°) = 1/tan(675°) = 1/tan(675° - 360°) = 1/tan(315°)
In the fourth quadrant, the tangent function is positive, so we find the reference angle for 315°:
315° - 270° = 45°
This means that tan(315°) = tan(45°) = 1, and therefore ctg(675°) = 1.
Putting it all together:
-810° + cos 900° - ctg 675° = -1 + (-1) - 1 = -3
Therefore, the final answer is -3.