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Trigonometric functions: Difference between revisions
→{{header|Ruby}}: Add alternate solution using 'bigdecimal'.
(→{{header|C}}: Add bc.) |
(→{{header|Ruby}}: Add alternate solution using 'bigdecimal'.) |
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0.785398163397 45.0
</pre>
=== {{libheader|bigdecimal}} ===
If you want more digits in the answer, then you can use the <tt>BigDecimal</tt> class. <tt>BigMath</tt> only has big versions of sine, cosine, and arctangent; so we must implement tangent, arcsine and arccosine.
{{trans|bc}}
{{works with|Ruby|1.9}}
<lang ruby>require 'bigdecimal' # BigDecimal
require 'bigdecimal/math' # BigMath
include BigMath # Allow sin(x, prec) instead of BigMath.sin(x, prec).
# Tangent of _x_.
def tan(x, prec)
sin(x, prec) / cos(x, prec)
end
# Arcsine of _y_, domain [-1, 1], range [-pi/2, pi/2].
def asin(y, prec)
# Handle angles with no tangent.
return -PI / 2 if y == -1
return PI / 2 if y == 1
# Tangent of angle is y / x, where x^2 + y^2 = 1.
atan(y / sqrt(1 - y * y, prec), prec)
end
# Arccosine of _x_, domain [-1, 1], range [0, pi].
def acos(x, prec)
# Handle angle with no tangent.
return PI / 2 if x == 0
# Tangent of angle is y / x, where x^2 + y^2 = 1.
a = atan(sqrt(1 - x * x, prec) / x, prec)
if a < 0
a + PI(prec)
else
a
end
end
prec = 52
pi = PI(prec)
degrees = pi / 180 # one degree in radians
b1 = BigDecimal.new "1"
b2 = BigDecimal.new "2"
b3 = BigDecimal.new "3"
f = proc { |big| big.round(50).to_s('F') }
print("Using radians:",
"\n sin(-pi / 6) = ", f[ sin(-pi / 6, prec) ],
"\n cos(3 * pi / 4) = ", f[ cos(3 * pi / 4, prec) ],
"\n tan(pi / 3) = ", f[ tan(pi / 3, prec) ],
"\n asin(-1 / 2) = ", f[ asin(-b1 / 2, prec) ],
"\n acos(-sqrt(2) / 2) = ", f[ acos(-sqrt(b2, prec) / 2, prec) ],
"\n atan(sqrt(3)) = ", f[ atan(sqrt(b3, prec), prec) ],
"\n")
print("Using degrees:",
"\n sin(-30) = ", f[ sin(-30 * degrees, prec) ],
"\n cos(135) = ", f[ cos(135 * degrees, prec) ],
"\n tan(60) = ", f[ tan(60 * degrees, prec) ],
"\n asin(-1 / 2) = ",
f[ asin(-b1 / 2, prec) / degrees ],
"\n acos(-sqrt(2) / 2) = ",
f[ acos(-sqrt(b2, prec) / 2, prec) / degrees ],
"\n atan(sqrt(3)) = ",
f[ atan(sqrt(b3, prec), prec) / degrees ],
"\n")</lang>
Output: <pre>Using radians:
sin(-pi / 6) = -0.5
cos(3 * pi / 4) = -0.70710678118654752440084436210484903928483593768847
tan(pi / 3) = 1.73205080756887729352744634150587236694280525381038
asin(-1 / 2) = -0.52359877559829887307710723054658381403286156656252
acos(-sqrt(2) / 2) = 2.35619449019234492884698253745962716314787704953133
atan(sqrt(3)) = 1.04719755119659774615421446109316762806572313312504
Using degrees:
sin(-30) = -0.5
cos(135) = -0.70710678118654752440084436210484903928483593768847
tan(60) = 1.73205080756887729352744634150587236694280525381038
asin(-1 / 2) = -30.0
acos(-sqrt(2) / 2) = 135.0
atan(sqrt(3)) = 60.0</pre>
=={{header|Scheme}}==
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