diff --git a/r/NEWS.md b/r/NEWS.md
index 83d09157b9038..a01a9217a4329 100644
--- a/r/NEWS.md
+++ b/r/NEWS.md
@@ -19,6 +19,10 @@
 
 # arrow 18.1.0.9000
 
+## Minor improvements and fixes
+
+- Added bindings for atan, sinh, cosh, tanh, asinh, acosh, and tanh, and expm1 (#44953)
+
 # arrow 18.1.0
 
 ## Minor improvements and fixes
diff --git a/r/R/arrow-datum.R b/r/R/arrow-datum.R
index ba513ef470cfb..8f532fb522c20 100644
--- a/r/R/arrow-datum.R
+++ b/r/R/arrow-datum.R
@@ -128,6 +128,7 @@ Math.ArrowDatum <- function(x, ..., base = exp(1), digits = 0) {
     log10 = eval_array_expression("log10_checked", x),
     log2 = eval_array_expression("log2_checked", x),
     log1p = eval_array_expression("log1p_checked", x),
+    expm1 = eval_array_expression("expm1", x),
     round = eval_array_expression(
       "round",
       x,
@@ -139,17 +140,16 @@ Math.ArrowDatum <- function(x, ..., base = exp(1), digits = 0) {
     cumprod = eval_array_expression("cumulative_prod_checked", x),
     cummax = eval_array_expression("cumulative_max", x),
     cummin = eval_array_expression("cumulative_min", x),
+    cosh = eval_array_expression("cosh", x),
+    sinh = eval_array_expression("sinh", x),
+    tanh = eval_array_expression("tanh", x),
+    acosh = eval_array_expression("acosh_checked", x),
+    asinh = eval_array_expression("asinh", x),
+    atanh = eval_array_expression("atanh_checked", x),
     signif = ,
-    expm1 = ,
     cospi = ,
     sinpi = ,
     tanpi = ,
-    cosh = ,
-    sinh = ,
-    tanh = ,
-    acosh = ,
-    asinh = ,
-    atanh = ,
     lgamma = ,
     gamma = ,
     digamma = ,
diff --git a/r/R/dplyr-funcs-doc.R b/r/R/dplyr-funcs-doc.R
index 4f90dd16b266f..470c89ecc3dff 100644
--- a/r/R/dplyr-funcs-doc.R
+++ b/r/R/dplyr-funcs-doc.R
@@ -21,7 +21,7 @@
 #'
 #' The `arrow` package contains methods for 37 `dplyr` table functions, many of
 #' which are "verbs" that do transformations to one or more tables.
-#' The package also has mappings of 212 R functions to the corresponding
+#' The package also has mappings of 221 R functions to the corresponding
 #' functions in the Arrow compute library. These allow you to write code inside
 #' of `dplyr` methods that call R functions, including many in packages like
 #' `stringr` and `lubridate`, and they will get translated to Arrow and run
@@ -42,7 +42,7 @@
 #' * [`collect()`][dplyr::collect()]
 #' * [`compute()`][dplyr::compute()]
 #' * [`count()`][dplyr::count()]
-#' * [`distinct()`][dplyr::distinct()]: `.keep_all = TRUE` not supported
+#' * [`distinct()`][dplyr::distinct()]: `.keep_all = TRUE` returns a non-missing value if present, only returning missing values if all are missing.
 #' * [`explain()`][dplyr::explain()]
 #' * [`filter()`][dplyr::filter()]
 #' * [`full_join()`][dplyr::full_join()]: the `copy` argument is ignored
@@ -83,7 +83,7 @@
 #' Functions can be called either as `pkg::fun()` or just `fun()`, i.e. both
 #' `str_sub()` and `stringr::str_sub()` work.
 #'
-#' In addition to these functions, you can call any of Arrow's 262 compute
+#' In addition to these functions, you can call any of Arrow's 271 compute
 #' functions directly. Arrow has many functions that don't map to an existing R
 #' function. In other cases where there is an R function mapping, you can still
 #' call the Arrow function directly if you don't want the adaptations that the R
@@ -96,6 +96,7 @@
 #'
 #' * [`add_filename()`][arrow::add_filename()]
 #' * [`cast()`][arrow::cast()]
+#' * [`one()`][arrow::one()]
 #'
 #' ## base
 #'
@@ -119,6 +120,7 @@
 #' * [`^`][^()]
 #' * [`abs()`][base::abs()]
 #' * [`acos()`][base::acos()]
+#' * [`acosh()`][base::acosh()]
 #' * [`all()`][base::all()]
 #' * [`any()`][base::any()]
 #' * [`as.Date()`][base::as.Date()]: Multiple `tryFormats` not supported in Arrow.
@@ -130,14 +132,19 @@
 #' * [`as.logical()`][base::as.logical()]
 #' * [`as.numeric()`][base::as.numeric()]
 #' * [`asin()`][base::asin()]
+#' * [`asinh()`][base::asinh()]
+#' * [`atan()`][base::atan()]
+#' * [`atanh()`][base::atanh()]
 #' * [`ceiling()`][base::ceiling()]
 #' * [`cos()`][base::cos()]
+#' * [`cosh()`][base::cosh()]
 #' * [`data.frame()`][base::data.frame()]: `row.names` and `check.rows` arguments not supported;
 #' `stringsAsFactors` must be `FALSE`
 #' * [`difftime()`][base::difftime()]: only supports `units = "secs"` (the default);
 #' `tz` argument not supported
 #' * [`endsWith()`][base::endsWith()]
 #' * [`exp()`][base::exp()]
+#' * [`expm1()`][base::expm1()]
 #' * [`floor()`][base::floor()]
 #' * [`format()`][base::format()]
 #' * [`grepl()`][base::grepl()]
@@ -171,6 +178,7 @@
 #' * [`round()`][base::round()]
 #' * [`sign()`][base::sign()]
 #' * [`sin()`][base::sin()]
+#' * [`sinh()`][base::sinh()]
 #' * [`sqrt()`][base::sqrt()]
 #' * [`startsWith()`][base::startsWith()]
 #' * [`strftime()`][base::strftime()]
@@ -183,6 +191,7 @@
 #' * [`substring()`][base::substring()]
 #' * [`sum()`][base::sum()]
 #' * [`tan()`][base::tan()]
+#' * [`tanh()`][base::tanh()]
 #' * [`tolower()`][base::tolower()]
 #' * [`toupper()`][base::toupper()]
 #' * [`trunc()`][base::trunc()]
diff --git a/r/R/dplyr-funcs-simple.R b/r/R/dplyr-funcs-simple.R
index 4ccc2498435b3..05780721f2410 100644
--- a/r/R/dplyr-funcs-simple.R
+++ b/r/R/dplyr-funcs-simple.R
@@ -32,14 +32,22 @@
   "base::log1p" = "log1p_checked",
   "base::log2" = "log2_checked",
   "base::sign" = "sign",
+  "base::expm1" = "expm1",
   # trunc is defined in dplyr-functions.R
 
   # trigonometric functions
   "base::acos" = "acos_checked",
   "base::asin" = "asin_checked",
   "base::cos" = "cos_checked",
+  "base::atan" = "atan",
   "base::sin" = "sin_checked",
   "base::tan" = "tan_checked",
+  "base::cosh" = "cosh",
+  "base::sinh" = "sinh",
+  "base::tanh" = "tanh",
+  "base::acosh" = "acosh_checked",
+  "base::asinh" = "asinh",
+  "base::atanh" = "atanh_checked",
 
   # logical functions
   "!" = "invert",
diff --git a/r/extra-tests/helpers.R b/r/extra-tests/helpers.R
deleted file mode 100644
index 3fb450ee33272..0000000000000
--- a/r/extra-tests/helpers.R
+++ /dev/null
@@ -1,36 +0,0 @@
-# Licensed to the Apache Software Foundation (ASF) under one
-# or more contributor license agreements.  See the NOTICE file
-# distributed with this work for additional information
-# regarding copyright ownership.  The ASF licenses this file
-# to you under the Apache License, Version 2.0 (the
-# "License"); you may not use this file except in compliance
-# with the License.  You may obtain a copy of the License at
-#
-#   http://www.apache.org/licenses/LICENSE-2.0
-#
-# Unless required by applicable law or agreed to in writing,
-# software distributed under the License is distributed on an
-# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
-# KIND, either express or implied.  See the License for the
-# specific language governing permissions and limitations
-# under the License.
-
-if_version <- function(version, op = `==`) {
-  op(packageVersion("arrow"), version)
-}
-
-if_version_less_than <- function(version) {
-  if_version(version, op = `<`)
-}
-
-skip_if_version_less_than <- function(version, msg) {
-  if (if_version(version, `<`)) {
-    skip(msg)
-  }
-}
-
-skip_if_version_equals <- function(version, msg) {
-  if (if_version(version, `==`)) {
-    skip(msg)
-  }
-}
diff --git a/r/extra-tests/test-read-files.R b/r/extra-tests/test-read-files.R
index 4201e00d7c314..2f5db38e52044 100644
--- a/r/extra-tests/test-read-files.R
+++ b/r/extra-tests/test-read-files.R
@@ -18,6 +18,8 @@
 library(arrow)
 library(testthat)
 
+source("tests/testthat/helper-skip.R")
+
 pq_file <- "files/ex_data.parquet"
 
 test_that("Can read the file (parquet)", {
@@ -30,7 +32,7 @@ test_that("Can read the file (parquet)", {
 
 ### Parquet
 test_that("Can see the metadata (parquet)", {
-  skip_if_version_less_than("2.0.0", "Version 1.0.1 can't read new version metadata.")
+  skip_if_arrow_version_less_than("2.0.0", "Version 1.0.1 can't read new version metadata.")
 
   df <- read_parquet(pq_file)
   expect_s3_class(df, "tbl")
@@ -74,7 +76,7 @@ for (comp in c("lz4", "uncompressed", "zstd")) {
   })
 
   test_that(paste0("Can see the metadata (feather ", comp, ")"), {
-    skip_if_version_less_than("2.0.0", "Version 1.0.1 can't read new version metadata.")
+    skip_if_arrow_version_less_than("2.0.0", "Version 1.0.1 can't read new version metadata.")
 
     df <- read_feather(feather_file)
     expect_s3_class(df, "tbl")
@@ -132,7 +134,7 @@ test_that("Can read the file (parquet)", {
 })
 
 test_that("Can see the metadata (stream)", {
-  skip_if_version_less_than("2.0.0", "Version 1.0.1 can't read new version metadata.")
+  skip_if_arrow_version_less_than("2.0.0", "Version 1.0.1 can't read new version metadata.")
   df <- read_ipc_stream(stream_file)
 
   expect_s3_class(df, "tbl")
diff --git a/r/tests/testthat/helper-skip.R b/r/tests/testthat/helper-skip.R
index bd29080848184..da48910133469 100644
--- a/r/tests/testthat/helper-skip.R
+++ b/r/tests/testthat/helper-skip.R
@@ -124,6 +124,26 @@ skip_on_python_older_than <- function(python_version) {
   }
 }
 
+if_arrow_version <- function(version, op = `==`) {
+  op(packageVersion("arrow"), version)
+}
+
+if_arrow_version_less_than <- function(version) {
+  if_version(version, op = `<`)
+}
+
+skip_if_arrow_version_less_than <- function(version, msg) {
+  if (if_arrow_version(version, `<`)) {
+    skip(msg)
+  }
+}
+
+skip_if_arrow_version_equals <- function(version, msg) {
+  if (if_arrow_version(version, `==`)) {
+    skip(msg)
+  }
+}
+
 process_is_running <- function(x) {
   if (force_tests()) {
     # Return TRUE as this is used as a condition in an if statement
diff --git a/r/tests/testthat/test-compute-arith.R b/r/tests/testthat/test-compute-arith.R
index 22c4ee8002e7a..602e718b71c5e 100644
--- a/r/tests/testthat/test-compute-arith.R
+++ b/r/tests/testthat/test-compute-arith.R
@@ -223,22 +223,32 @@ test_that("Math group generics work on Array objects", {
   )
 
   expect_error(signif(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
-  expect_error(expm1(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
 
   expect_error(cospi(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
   expect_error(sinpi(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
   expect_error(tanpi(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
 
-  expect_error(cosh(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
-  expect_error(sinh(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
-  expect_error(tanh(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
-
-  expect_error(acosh(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
-  expect_error(asinh(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
-  expect_error(atanh(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
-
   expect_error(lgamma(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
   expect_error(gamma(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
   expect_error(digamma(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
   expect_error(trigamma(Array$create(c(4L, 1L))), "Unsupported operation on `Array`")
 })
+
+test_that("hyperbolic trig functions work on Array objects", {
+  skip_if_arrow_version_less_than("18.1.0.9000", "Hyperbolic trig functions not available until version 19.")
+
+  expect_equal(sinh(Array$create(c(0.6, 0.9))), Array$create(sinh(c(0.6, 0.9))))
+  expect_equal(cosh(Array$create(c(0.6, 0.9))), Array$create(cosh(c(0.6, 0.9))))
+  expect_equal(tanh(Array$create(c(0.6, 0.9))), Array$create(tanh(c(0.6, 0.9))))
+  expect_equal(asinh(Array$create(c(0.6, 0.9))), Array$create(asinh(c(0.6, 0.9))))
+  expect_error(acosh(Array$create(c(0.6, 0.9))), "Invalid: domain error")
+  expect_equal(acosh(Array$create(c(1, 2))), Array$create(acosh(c(1, 2))))
+  expect_error(atanh(Array$create(c(-1, 1))), "Invalid: domain error")
+  expect_equal(atanh(Array$create(c(0.6, 0.9))), Array$create(atanh(c(0.6, 0.9))))
+})
+
+test_that("expm1 works on Array objects", {
+  skip_if_arrow_version_less_than("18.1.0.9000", "expm1 not available until version 19.")
+
+  expect_equal(expm1(Array$create(c(0.00000001, 10))), Array$create(expm1(c(0.00000001, 10))))
+})
diff --git a/r/tests/testthat/test-dplyr-funcs-math.R b/r/tests/testthat/test-dplyr-funcs-math.R
index 1057f7ae06eb0..bed2da110ba4b 100644
--- a/r/tests/testthat/test-dplyr-funcs-math.R
+++ b/r/tests/testthat/test-dplyr-funcs-math.R
@@ -315,6 +315,13 @@ test_that("trig functions", {
     df
   )
 
+    compare_dplyr_binding(
+    .input %>%
+      mutate(y = atan(x)) %>%
+      collect(),
+    df
+  )
+
   # with namespacing
   compare_dplyr_binding(
     .input %>%
@@ -323,7 +330,94 @@ test_that("trig functions", {
         b = base::cos(x),
         c = base::tan(x),
         d = base::asin(x),
-        e = base::acos(x)
+        e = base::acos(x),
+        f = base::atan(x)
+      ) %>%
+      collect(),
+    df
+  )
+})
+
+test_that("hyperbolic trig functions", {
+  skip_if_arrow_version_less_than("18.1.0.9000", "Hyperbolic trig functions not available until version 19.")
+
+  # Note: We change df mid-test because domains differ by function
+  df <- tibble(x = c(seq(from = 0, to = 1, by = 0.1), NA))
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(y = sinh(x)) %>%
+      collect(),
+    df
+  )
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(y = cosh(x)) %>%
+      collect(),
+    df
+  )
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(y = tanh(x)) %>%
+      collect(),
+    df
+  )
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(y = asinh(x)) %>%
+      collect(),
+    df
+  )
+
+  # with namespacing
+  compare_dplyr_binding(
+    .input %>%
+      mutate(
+        a = base::sinh(x),
+        b = base::cosh(x),
+        c = base::tanh(x),
+        d = base::asinh(x),
+      ) %>%
+      collect(),
+    df
+  )
+
+  df <- tibble(x = c(seq(from = 1, to = 2, by = 0.1)))
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(y = acosh(x)) %>%
+      collect(),
+    df
+  )
+
+  # with namespacing
+  compare_dplyr_binding(
+    .input %>%
+      mutate(
+        a = base::acosh(x),
+      ) %>%
+      collect(),
+    df
+  )
+
+  df <- tibble(x = c(seq(from = -0.5, to = 0.5, by = 0.1)))
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(y = atanh(x)) %>%
+      collect(),
+    df
+  )
+
+  # with namespacing
+  compare_dplyr_binding(
+    .input %>%
+      mutate(
+        a = base::atanh(x)
       ) %>%
       collect(),
     df
@@ -399,3 +493,19 @@ test_that("sqrt()", {
     df
   )
 })
+
+test_that("expm1()", {
+  skip_if_arrow_version_less_than("18.1.0.9000", "expm1 not available until version 19.")
+
+  df <- tibble(x = c(1:5))
+
+  compare_dplyr_binding(
+    .input %>%
+      mutate(
+        y = expm1(x),
+        y2 = base::expm1(x)
+      ) %>%
+      collect(),
+    df
+  )
+})