---
.../elementary/tests/test_trigonometric.py | 8 +++++++-
sympy/functions/elementary/trigonometric.py | 16 ++++++++++++----
2 files changed, 19 insertions(+), 5 deletions(-)
diff --git a/sympy/functions/elementary/tests/test_trigonometric.py
b/sympy/functions/elementary/tests/test_trigonometric.py
index 37b05c0..ade2aca 100644
--- a/sympy/functions/elementary/tests/test_trigonometric.py
+++ b/sympy/functions/elementary/tests/test_trigonometric.py
@@ -266,9 +266,15 @@ def test_asin():
assert asin(-oo) == I*oo
assert asin(0) == 0
- assert asin(Rational(1,2)) == pi/6
assert asin(1) == pi/2
assert asin(sqrt(3)/2) == pi/3
+ assert asin(sqrt(2)/2) == pi/4
+ assert asin(sqrt((5-sqrt(5))/8)) == pi/5
+ assert asin(Rational(1,2)) == pi/6
+ assert asin((sqrt(2-sqrt(2)))/2) == pi/8
+ assert asin((sqrt(5)-1)/4) == pi/10
+ assert asin((sqrt(3)-1)/sqrt(2**3)) == pi/12
+
assert asin(x).diff(x) == 1/sqrt(1-x**2)
diff --git a/sympy/functions/elementary/trigonometric.py
b/sympy/functions/elementary/trigonometric.py
index 9b39016..5c4c1b9 100644
--- a/sympy/functions/elementary/trigonometric.py
+++ b/sympy/functions/elementary/trigonometric.py
@@ -801,14 +801,22 @@ def eval(cls, arg):
if arg.is_number:
cst_table = {
- S.Half : 6,
- -S.Half : -6,
+ sqrt(3)/2 : 3,
+ -sqrt(3)/2 : -3,
sqrt(2)/2 : 4,
-sqrt(2)/2 : -4,
1/sqrt(2) : 4,
-1/sqrt(2) : -4,
- sqrt(3)/2 : 3,
- -sqrt(3)/2 : -3,
+ sqrt((5-sqrt(5))/8) : 5,
+ -sqrt((5-sqrt(5))/8) : -5,
+ S.Half : 6,
+ -S.Half : -6,
+ sqrt(2-sqrt(2))/2 : 8,
+ -sqrt(2-sqrt(2))/2 : -8,
+ (sqrt(5)-1)/4 : 10,
+ (1-sqrt(5))/4 : -10,
+ (sqrt(3)-1)/sqrt(2**3) : 12,
+ (1-sqrt(3))/sqrt(2**3) : -12,
}
if arg in cst_table:
--
1.7.0.4
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