1, power decreasing formula of trigonometric function:
Sin? α=( 1-cos2α)/2
Because? α=( 1+cos2α)/2
Tan? α=( 1-cos2α)/( 1+cos2α)
2. The derivation process of trigonometric function power-down formula
The angle-doubling formula is used to improve the power, and the formula cos2α can be modified to obtain the formula for reducing the power:
cos2α=cos？ α-sin？ α=2cos？ α- 1= 1-2sin？ α
∴cos？ α=( 1+cos2α)/2
Sin? α=( 1-cos2α)/2
The formula of decreasing power is the formula of decreasing exponential power from quadratic to 1, which can reduce the trouble of quadratic.
Origin of trigonometric function
From the 5th century to12nd century, Indian mathematicians made great contributions to trigonometry. Although trigonometry was still a computing tool and an accessory of astronomy at that time, the content of trigonometry was greatly enriched through the efforts of Indian mathematicians.
The concepts of sine and cosine in trigonometry were first introduced by Indian mathematicians, who also made sine tables more accurate than Ptolemy.
As we already know, the chord table created by Ptolemy and Hipparchus is a circular full chord table, which corresponds to arcs and chords sandwiched between arcs. Unlike Indian mathematicians, they correspond the half chord (AC) to the half arc (AD) of the whole chord, that is, AC corresponds to ∠AOC. In this way, they created a sine table instead of a full chord table.
Indians call the chord (AB) connecting the two ends of the arc (AB) "jiba", which means bowstring; One half (AC) of AB is called "Al Hajiwa". Later, when the word "Jiwa" was translated into Arabic, it was misunderstood as "bend" and "concave", and Arabic was "dschaib". /kloc-in the 0/2nd century, Arabic was translated into Latin, and the word was translated into "dou".
Refer to the above? Baidu encyclopedia-trigonometric function