diff --git a/examples/misc/custom_projection.py b/examples/misc/custom_projection.py
index 39fb58a1e768..fedee56a4be8 100644
--- a/examples/misc/custom_projection.py
+++ b/examples/misc/custom_projection.py
@@ -450,8 +450,7 @@ def _get_core_transform(self, resolution):
         return self.HammerTransform(resolution)
 
 
-# Now register the projection with matplotlib so the user can select
-# it.
+# Now register the projection with Matplotlib so the user can select it.
 register_projection(HammerAxes)
 
 
diff --git a/lib/matplotlib/axes/_axes.py b/lib/matplotlib/axes/_axes.py
index 2be35ddb5697..fd724f55876c 100644
--- a/lib/matplotlib/axes/_axes.py
+++ b/lib/matplotlib/axes/_axes.py
@@ -9,9 +9,7 @@
 import numpy as np
 from numpy import ma
 
-import matplotlib
-from matplotlib import _preprocess_data
-
+from matplotlib import _preprocess_data, rcParams
 import matplotlib.cbook as cbook
 import matplotlib.collections as mcoll
 import matplotlib.colors as mcolors
@@ -39,8 +37,6 @@
 
 _log = logging.getLogger(__name__)
 
-rcParams = matplotlib.rcParams
-
 
 def _make_inset_locator(bounds, trans, parent):
     """
diff --git a/lib/matplotlib/backends/backend_cairo.py b/lib/matplotlib/backends/backend_cairo.py
index d202f0494625..b14b94e91b76 100644
--- a/lib/matplotlib/backends/backend_cairo.py
+++ b/lib/matplotlib/backends/backend_cairo.py
@@ -6,7 +6,6 @@
 This backend depends on cairocffi or pycairo.
 """
 
-import copy
 import gzip
 
 import numpy as np
diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
index 8e2818f098e1..794fd61b7ca1 100644
--- a/lib/matplotlib/backends/backend_pdf.py
+++ b/lib/matplotlib/backends/backend_pdf.py
@@ -9,11 +9,10 @@
 from functools import total_ordering
 from io import BytesIO
 import logging
-from math import ceil, cos, floor, pi, sin
+import math
 import os
 import re
 import struct
-import sys
 import time
 import types
 import warnings
@@ -890,9 +889,9 @@ def cvt(length, upe=font.units_per_EM, nearest=True):
             # Perhaps best to round away from zero for bounding
             # boxes and the like
             if value < 0:
-                return floor(value)
+                return math.floor(value)
             else:
-                return ceil(value)
+                return math.ceil(value)
 
         def embedTTFType3(font, characters, descriptor):
             """The Type 3-specific part of embedding a Truetype font"""
@@ -1818,9 +1817,9 @@ def _setup_textpos(self, x, y, angle, oldx=0, oldy=0, oldangle=0):
         if angle == oldangle == 0:
             self.file.output(x - oldx, y - oldy, Op.textpos)
         else:
-            angle = angle / 180.0 * pi
-            self.file.output(cos(angle), sin(angle),
-                             -sin(angle), cos(angle),
+            angle = math.radians(angle)
+            self.file.output(math.cos(angle), math.sin(angle),
+                             -math.sin(angle), math.cos(angle),
                              x, y, Op.textmatrix)
             self.file.output(0, 0, Op.textpos)
 
@@ -1836,10 +1835,11 @@ def draw_mathtext(self, gc, x, y, s, prop, angle):
         global_fonttype = rcParams['pdf.fonttype']
 
         # Set up a global transformation matrix for the whole math expression
-        a = angle / 180.0 * pi
+        a = math.radians(angle)
         self.file.output(Op.gsave)
-        self.file.output(cos(a), sin(a), -sin(a), cos(a), x, y,
-                         Op.concat_matrix)
+        self.file.output(math.cos(a), math.sin(a),
+                         -math.sin(a), math.cos(a),
+                         x, y, Op.concat_matrix)
 
         self.check_gc(gc, gc._rgb)
         self.file.output(Op.begin_text)
@@ -2058,9 +2058,10 @@ def draw_text_woven(chunks):
             # Do the rotation and global translation as a single matrix
             # concatenation up front
             self.file.output(Op.gsave)
-            a = angle / 180.0 * pi
-            self.file.output(cos(a), sin(a), -sin(a), cos(a), x, y,
-                             Op.concat_matrix)
+            a = math.radians(angle)
+            self.file.output(math.cos(a), math.sin(a),
+                             -math.sin(a), math.cos(a),
+                             x, y, Op.concat_matrix)
 
             # Output all the 1-byte characters in a BT/ET group, then
             # output all the 2-byte characters.
diff --git a/lib/matplotlib/projections/polar.py b/lib/matplotlib/projections/polar.py
index 815653927b6e..b62edf181319 100644
--- a/lib/matplotlib/projections/polar.py
+++ b/lib/matplotlib/projections/polar.py
@@ -2,7 +2,6 @@
 import types
 
 import numpy as np
-import warnings
 
 from matplotlib.axes import Axes
 import matplotlib.axis as maxis
diff --git a/lib/matplotlib/tight_layout.py b/lib/matplotlib/tight_layout.py
index 06ab3927ec57..68b1e70c0bcb 100644
--- a/lib/matplotlib/tight_layout.py
+++ b/lib/matplotlib/tight_layout.py
@@ -9,12 +9,9 @@
 for some cases (for example, left or right margin is affected by xlabel).
 """
 
-import matplotlib
-from matplotlib import cbook
-from matplotlib.transforms import TransformedBbox, Bbox
-
+from matplotlib import cbook, rcParams
 from matplotlib.font_manager import FontProperties
-rcParams = matplotlib.rcParams
+from matplotlib.transforms import TransformedBbox, Bbox
 
 
 def _get_left(tight_bbox, axes_bbox):