What seven points of x can I put on the x axis over the interval -2pi less than or equal to x less than or equal to 2pi
Is the exact value of sin(pi/3) + cos(pi/6) equal to 1.73?
I do not understand Randy's question.
Anna
sin (pi/3) = (1/2) sqrt 3
cos (pi/6) = (1/2) sqrt 3
sum = sqrt 3 exactly
However sqrt 3 is an irrational number. It can not be expressed exactly by 1.73 or 1.732050808 or any other integer plus decimal fraction
SO my answer would be sqrt 3?
If you are supposed to give exact answer, the only one is sqrt 3
To find seven points on the x-axis over the given interval, we can divide the interval -2π ≤ x ≤ 2π into equal intervals and represent them as angles around the unit circle.
1. Start by dividing the interval into 14 equal parts, since there are 2π radians in a full circle.
2. Determine the size of each interval by dividing the total range (2π) by the number of intervals (14). In this case, each interval would be 2π/14.
3. Choose a starting point within the interval. Let's use -2π as the starting point.
4. Add the interval size repeatedly to the starting point to get the coordinates on the x-axis.
5. Repeat this process until you have obtained seven distinct points.
Using this method, the seven points on the x-axis can be obtained as follows:
Point 1: -2π
Point 2: -2π + (2π/14) = -27π/14
Point 3: -2π + (4π/14) = -25π/14
Point 4: -2π + (6π/14) = -23π/14
Point 5: -2π + (8π/14) = -21π/14
Point 6: -2π + (10π/14) = -19π/14
Point 7: -2π + (12π/14) = -17π/14
Therefore, the seven points on the x-axis over the interval -2π ≤ x ≤ 2π are:
-2π, -27π/14, -25π/14, -23π/14, -21π/14, -19π/14, -17π/14.