The section of shofaros starts with "Ata nigleysa" "You revealed yourself...". The first verse used in the ten shofaros verses is a pasuk from Torah (Exodus 19:16) "VaYehi bayom hashlishi..." "And it was on the third day...". The tenth verse used is one from the Prophets (Zechariah 9:14) "VaHashem aleyhem yeraeh..." "And G-d appeared unto them...".
The tenth verse mentions the shofar. "...and G-d sounded with the shofar..."
The machzor then has the key words "Elokeinu vEylokei avoseinu" to indicate that the 10 verses are over and the chazzan is now continuing with a special request poem connected with shofar leading to the brachah of shofaros. Along the way, a pasuk from Torah (Numbers 10:10) is used to stress the poem's point, that we should all experience happiness on the holiday when we offer karbanos. This pasuk mentions trumpets but not shofar. That is because it is not one of the ten pasukim of shofaros.
The 4th verse of shofaros mentions trumpets and shofar (Psalms 98:6)
There is a connection to trumpets and shofar as both were combined in the Temple service (based on Psalms 98:6). See Mishnah Rosh HaShannah 3:3-4.
Apparently, our machzorim are not strict about the 10th verse being from Torah specifically (as opposed to Prophets or Writings).
Hope this helps.
Hi all, The above answer is wrong. I do not know protocol here for this so I would appreciate the help. Should it be deleted? etc.
Here are my 3 basic mistakes:
1) Numbers 10:10 is in fact the final Torah verse of shofaros. I was wrong to assume that since it looked like the 11th, that it was not part of the ten. The Psalm 150 is the addition.
2) Double AA is correct. The key words Elokeinu VElokei avoseinu (although usually does introduce a new section in davening) does not preclude the 10th verse from being saved for that paragraph. He is right from the example that Zichronos does the same thing. The trick is that Malchiot does not allow its tenth verse in the Elokeinu VElokei avosenu paragraph.
3) Our machzorim do in fact make sure that the tenth or final verse is from Torah (not Navi or Ketuvim).
Thanks also to DanF and msh210 for notes that got me thinking along with Double AA.
The real answer is that :
1) The final verse of each set is meant to appear in the final brachah paragraph. The exception is malchiot; for a special reason.
2) The Psalm 150 is included as an 11th verse in shofaros due to its midrashic value of being the source for learning that we need ten.
3) The trumpets verse that the OP originally asked about (due to its lack of mention of the key word "shofar"), Numbers 10:10, is used anyway due to it being a major source drashah for the origin of the obligation of Malchiut, Zichronos, and Shofaros in the first place. Some say that Psalm 150 was added to make up for Numbers 10 lacking the word shofar.
I did research this last night to find this all out. However, some of it is still unclear to me and I have not verified the sources yet, so I am just providing short notes above with my retraction.