## 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.