To find a negative angle that is coterminal with -70° and within the range greater than -720° but still negative, we must first understand what coterminal angles are.
Coterminal angles share the same initial and terminal sides. They can be found by adding or subtracting multiples of [tex]\(360^\circ\)[/tex] to the given angle.
Given:
[tex]\[
\text{Original angle } = -70^\circ
\][/tex]
To find a coterminal angle that falls within the desired range, we must subtract multiples of [tex]\(360^\circ\)[/tex] from [tex]\(-70^\circ\)[/tex] until we reach an angle greater than [tex]\(-720^\circ\)[/tex].
Let's find the first few coterminal angles by subtracting multiples of [tex]\(360^\circ\)[/tex]:
1. First coterminal angle:
[tex]\[
-70^\circ - 360^\circ = -430^\circ
\][/tex]
2. Second coterminal angle:
[tex]\[
-430^\circ - 360^\circ = -790^\circ
\][/tex]
However, [tex]\(-790^\circ\)[/tex] is less than [tex]\(-720^\circ\)[/tex], so it doesn't fit the requirement. Therefore, we need to use the coterminal angle of [tex]\(-430^\circ\)[/tex].
[tex]\(-430^\circ\)[/tex] satisfies the conditions of:
- Being coterminal with [tex]\(-70^\circ\)[/tex]
- Being negative
- Being greater than [tex]\(-720^\circ\)[/tex]
Thus, the negative angle greater than [tex]\(-720^\circ\)[/tex] that is coterminal with [tex]\(-70^\circ\)[/tex] is:
[tex]\[
-430^\circ
\][/tex]
In conclusion:
[tex]\[
-430^\circ
\][/tex]
