HP
Prime: Trigonometric CAS Rewrite
Commands
All of the
following examples have CAS Simplification set to Minimum.
Rewrites of
Arcsine and Sine
|
asin2acos
|
Toolbox →
4. Rewrite → 5. Sine → 1. asin x → acos x
|
asin2acos(2*asin(x))
returns
2*(-acos(x) + π/2)
|
|
asin2atan
|
Toolbox →
4. Rewrite → 5. Sine → 2. asin x → atan x
|
asin2atan(2*asin(x))
returns
2*(atan(x/√(-x^2+1))
|
|
sin2costan
|
Toolbox →
4. Rewrite → 5. Sine → 3. sin x → cos x tan x
|
sin2costan(2*sin(x)^2)
returns
2*(cos(x)*tan(x))^2
|
Rewrites of
Arcosine and Cosine
|
acos2asin
|
Toolbox →
4. Rewrite → 6. Cosine → 1. acos x → asin x
|
acos2asin(acos(x*π/2))
returns
-asin(1/2*π*x)+π/2
|
|
acos2atan
|
Toolbox →
4. Rewrite → 6. Cosine → 2. acos x → atan x
|
acos2atan(acos(x*π/2))
returns
-atan( (1/2*π*x)/
(√(1/4) –
√(-(π*x)^2+4)
)+π/2
|
|
cos2sintan
|
Toolbox →
4. Rewrite → 6. Cosine → 3. cos x → sin x/tan x
|
cos2sintan(2*cos(x)^2)
Returns
2*(sin(x)/tan(x))^2
|
Rewrites of
Arctangent and Tangent
|
atan2asin
|
Toolbox →
4. Rewrite → 7. Tangent → 1. atan x → asin x
|
atan2asin(atan(x/3))
returns
asin( (x/3) /
(√(1/9)*√(x^2+9))
simplify gets
asin( (x*√(x^2+9))
/
(x^2+9) )
|
|
atan2acos
|
Toolbox →
4. Rewrite → 7. Tangent → 2. atan x → acos x
|
atan2acos(atan(x/3))
returns
-acos( (x/3) /
(√(1/9)*√(x^2+9))+π/2
simplify gets
( (π-2*acos(
(x*√(x^2+9))/(x^2+9)
)/2
|
|
tan2sincos
|
Toolbox →
4. Rewrite → 7. Tangent → 3. tan x → sin x/cos x
|
tan2sincos(tan(2*x))
returns
sin(2*x)/cos(2*x)
|
|
halftan
(sin x,
cos x, tan x) → tan(x/2)
|
Toolbox →
4. Rewrite → 7. Tangent → 4. halftan
|
halftan(cos(2*x))
returns
(-tan(x)^2+1)/
(tan(x)^2+1)
|
Other
Commands
|
tlin
(trigonometric
form of powers) → (trigonometric form of linearized terms)
|
Toolbox →
4. Rewrite → 8. Trig → 5. tlin
|
tlin(cos(2*x)^2)
returns
1/2*cos(4*x)+1/2
|
|
trig2exp
(sin x,
cos x, tan x) → (exponential form with complex exponentials)
|
Toolbox →
4. Rewrite → 8. Trig → 8. trig2exp
|
trig2exp(sin(x/3))
returns
1/(2*i) *
(e^(i*x/3) – 1/e^(i*x/3))
|
|
atrig2ln
(asin x,
acos x, atan x) → (logarithm form with complex exponentials)
|
Toolbox →
4. Rewrite → 8. Trig → 4. atrig2ln
|
atrig2ln(asin(x/3))
returns
i*ln(√(1/9)*√(x^2-9)+x/3)+π/2
|
That is a
list of basic CAS commands for trigonometric rewrites.
Eddie
This blog is
property of Edward Shore, 2016.