Wednesday, June 8, 2016

HP Prime: Trigonometric CAS Rewrite Commands

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.

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