evaluate the trigonometry function using its period as an aid cos(-7pi/3)
7/3 = 2 1/3
2 pi is a full circle
so we have gone around clockwise two circles and pi/3
so we really want cos (-pi/3)
draw a picture of that,60 degrees below the x axis in quadrant 4
the cosine is cos -60 degrees which is 1/2
To evaluate the trigonometric function cos(-7π/3) using its period as an aid, we can use the fact that the cosine function has a period of 2π.
The given angle is -7π/3, which is a negative angle. To convert it into an equivalent angle between 0 and 2π, we can add 2π repeatedly until we obtain an angle within this range:
-7π/3 + 2π = -7π/3 + 6π/3 = -π/3
Now, we have an angle of -π/3, which is between 0 and 2π.
Next, we can evaluate the cosine function for this angle. The cosine function tells us the ratio between the adjacent side and the hypotenuse of an angle in a right triangle.
To evaluate cos(-π/3), we can use the unit circle or the reference angle in the first quadrant.
In the first quadrant, the reference angle for -π/3 is π/3. The cosine of π/3 is 1/2.
However, since the angle -π/3 is in the fourth quadrant, the cosine function is negative. Therefore, cos(-π/3) = -1/2.
So, cos(-7π/3) = -1/2.
To evaluate the trigonometric function cos(-7π/3), we can use the period of cosine as an aid.
The period of the cosine function is 2π, which means that the cosine function repeats itself every 2π radians.
To find an equivalent angle within one period (between 0 and 2π) for -7π/3, we can add or subtract multiples of the period until we get an angle within this range.
In this case, we can add 2π to -7π/3:
-7π/3 + 2π = -7π/3 + 6π/3 = -π/3
Now, we have found an equivalent angle within one period.
The cosine function at -π/3 can be evaluated to find the answer.