diff --git a/matrix.cpp b/matrix.cpp
index 1b57f388..4c4e0800 100644
--- a/matrix.cpp
+++ b/matrix.cpp
@@ -174,10 +174,11 @@ template <typename T>
 util::matrix4<T>
 util::perspective (T fov, T aspect, range<T> Z)
 {
+    CHECK_LIMIT (fov, 0, 2 * util::pi<T>);
     CHECK_GE (Z.lo, 0);
     CHECK_GE (Z.hi, 0);
 
-    T f = 1 / std::tan (fov / 2);
+    T f = cos (T{0.5} * fov) / sin (T{0.5} * fov);
 
     T  x = f / aspect;
     T  y = f;