(12C) Bhaskara's Sine and Cosine Approximations

07292022, 05:13 PM
Post: #3




RE: (12C) Bhaskara's Sine and Cosine Approximations
(07292022 12:13 PM)Thomas Klemm Wrote: The approximation for \(\cos(x)\) allows to find an approximation for \(\cos^{1}(x)\) as well: We don't have estimate formula for asin(x), because sin(x) were defined from estimated cos(x) In other words, OP sin estimate formula is not needed; it is same as cos(90°  x°)  We can define angle unit, ht = halfturn, to aid in memorization. With 1 ht = pi radian = 180 degree, we have: cos(x ht) ≈ (14x²) / (1+x²) acos(x) ≈ √( (1x) / (4+x) ) ht Example: cos(45°) ≈ cos(1/4 ht) = (14/16) / (1+1/16) = 12/17 ≈ 0.7059 acos(0.7059) ≈ √(0.2941 / 4.7059) ht ≈ 0.2500 ht = 45.00° 

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Messages In This Thread 
(12C) Bhaskara's Sine and Cosine Approximations  Thomas Klemm  02262022, 06:22 PM
RE: (12C) Bhaskara's Sine and Cosine Approximations  Thomas Klemm  07292022, 12:13 PM
RE: (12C) Bhaskara's Sine and Cosine Approximations  Albert Chan  07292022 05:13 PM
RE: (12C) Bhaskara's Sine and Cosine Approximations  Thomas Klemm  07302022, 10:51 AM

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