Cos 600º + sin 600º -?
since 600º = 360º+240º, you have
cos 240º + sin 240º
since 240º = 180º + 60º, you have
-cos 60º - sin 60º = -1/2 - √3/2 = -(1+√3)/2
To find the value of cos 600º and sin 600º, we will use the unit circle and the periodicity of trigonometric functions.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) on a coordinate plane. The angles are measured in degrees or radians, going counterclockwise.
To find the value of cos 600º, we must first recognize that 600º is one full revolution plus an additional 240º. Since one full revolution on the unit circle corresponds to an angle of 360º, we can subtract 360º from 600º to get the equivalent angle within one revolution: 600º - 360º = 240º.
So, cos 600º is equivalent to cos 240º. Looking at the unit circle, we see that cos 240º is the x-coordinate of the point corresponding to 240º. In this case, the x-coordinate is -0.5. Therefore, cos 600º = -0.5.
Similarly, to find the value of sin 600º using the unit circle, we can make the same observations. 600º is equivalent to 240º, which is one full revolution plus an additional 240º. So, sin 600º is the same as sin 240º, which is the y-coordinate of the point corresponding to 240º on the unit circle. In this case, the y-coordinate is -√3/2. Therefore, sin 600º = -√3/2.
Now, to find cos 600º + sin 600º, we simply substitute the values we found:
cos 600º + sin 600º = -0.5 + (-√3/2) = -0.5 - √3/2 = -(0.5 + √3/2).
So, the value of cos 600º + sin 600º is -(0.5 + √3/2).