Pygame Rotated Shooting

Here’s a quick’n’dirty executable example of how to use vector math to do what you want.

import pygame

class Player(pygame.sprite.Sprite):
    def __init__(self):
        super().__init__()
        self.image = pygame.Surface((32, 32))
        self.image.fill((0, 0, 0))
        self.image.set_colorkey((0, 0, 0))
        pygame.draw.polygon(self.image, pygame.Color('dodgerblue'), ((0, 0), (32, 16), (0, 32)))
        self.org_image = self.image.copy()
        self.angle = 0
        self.direction = pygame.Vector2(1, 0)
        self.rect = self.image.get_rect(center=(200, 200))
        self.pos = pygame.Vector2(self.rect.center)

    def update(self, events, dt):
        for e in events:
            if e.type == pygame.KEYDOWN:
                if e.key == pygame.K_SPACE:
                    self.groups()[0].add(Projectile(self.rect.center, self.direction.normalize()))
        pressed = pygame.key.get_pressed()
        if pressed[pygame.K_a]:
            self.angle += 3
        if pressed[pygame.K_d]:
            self.angle -= 3

        self.direction = pygame.Vector2(1, 0).rotate(-self.angle)
        self.image = pygame.transform.rotate(self.org_image, self.angle)
        self.rect = self.image.get_rect(center=self.rect.center)

class Projectile(pygame.sprite.Sprite):
    def __init__(self, pos, direction):
        super().__init__()
        self.image = pygame.Surface((8, 8))
        self.image.fill((0, 0, 0))
        self.image.set_colorkey((0, 0, 0))
        pygame.draw.circle(self.image, pygame.Color('orange'), (4, 4), 4)
        self.rect = self.image.get_rect(center=pos)
        self.direction = direction
        self.pos = pygame.Vector2(self.rect.center)

    def update(self, events, dt):
        self.pos += self.direction * dt
        self.rect.center = self.pos
        if not pygame.display.get_surface().get_rect().contains(self.rect):
            self.kill()

def main():
    pygame.init()
    screen = pygame.display.set_mode((500, 500))
    sprites = pygame.sprite.Group(Player())
    clock = pygame.time.Clock()
    dt = 0

    while True:
        events = pygame.event.get()
        for e in events:
            if e.type == pygame.QUIT:
                return
        sprites.update(events, dt)
        screen.fill((30, 30, 30))
        sprites.draw(screen)
        pygame.display.update()
        dt = clock.tick(60)

if __name__ == '__main__':
    main()

Note: it seems that you’re loading the image of your player every frame. You should not do that, as this is very slow. Just load each image once. Also, it’s better to have only one spot in your code that calls pygame.display.update(), as you should make sure it’s called only once each frame.