Draw the wanted frame in Illustrator. You can for ex. align 2 circles and lines. Then fill the wanted piece with the Shape builder. Delete the extra parts and use the frame as the top object in Object > Envelope Distort > Make with Top Object.
It's tried here:
The lines were originally vertical, they are rotated plus and minus 30 degrees to get 60 degrees sector.
You must have right drawing dimensions to avoid losing resolution when you export the result as PNG or JPG. You can also copy and paste it to Photoshop straight from Illustrator. Before pasting open a big enough (in pixels) new document in Photoshop.
Photoshop can also make the warping. You can use Edit > Transform > Warp > Arc with negative percentage. In your case the right percentage is -33,3%. That's because 60 degrees is 33,3% of 180 degrees.
To get the wanted radiuses you must before warping stretch, squeeze or crop the image to certain dimensions and be sure that the photo is a freely deformable layer, not locked like the background.
The latter is required because the generated warped layer is bigger than the image size.
Let's assume you want sector angle = A, inner radius = R and outer radius = Q. With elementary trigonometry you get the following formulas to the needed rectangular image size before warping.
Width: W=2Rsin(A/2) Height: H=Q-R
If R=50 mm Q=150 mm and A=60 degrees, then W=50 mm and H=100 mm.
The layer size will be much bigger. New width will be W2=2Qsin(A/2). New height will be H2=Q-Rcos(A/2)
The next image has our Penguin photo stretched to 50 x 100 millimeters and warped to -33,3 % Arc. You see the result is much bigger:
In your case W2=150 millimeters and H2=106,7 millimeters. You must resize the canvas to this size.
This is the canvas resizing dialog:
And this is the resized image:
NOTE: Photoshop rounds image dimensions to full pixels. Thus it's well possible that the image is one pixel width too big or small. I guess the error is unnoticeable even at screen resolution.
There's a comment "you need a script". For it a programmer is needed. Unfortunately I'm not one.