Let the minimum positive period of the square of the function FX = sinwx + 2 times root sign three sin2 / Wx be 2 / 3 π, and find the analytic expression of the function FX

Let the minimum positive period of the square of the function FX = sinwx + 2 times root sign three sin2 / Wx be 2 / 3 π, and find the analytic expression of the function FX

FX = sinwx + 2 times the square of root sign three sin2 / Wx = sinwx + 2 √ 3sin & # 178; (Wx / 2) = sinwx + √ 3 [2Sin & # 178; (Wx / 2) - 1] + √ 3 = sinwx - √ 3coswx + √ 3 = 2 (1 / 2sinwx - √ 3 / 2coswx) + √ 3 = 2Sin (Wx - π / 3) + √ 3 ∵ the minimum positive period is 2 π / (2 π / 3) = 3 ∵ F
F (x) = sinwx + radical 3 * (1-coswx) = sinwx - radical 3coswx + radical 3 = 2 (1 / 2sinwx - radical 3 / 2coswx) + radical 3
=2Sin (Wx Pai / 3) + radical 3
T=2Pai/w=2Pai/3
W=3
F (x) = 2Sin (3x Pai / 3) + radical 3
It is known that the minimum positive period of F (x) = Sin & sup2; Wx + radical 3 sinwx sin (Wx + π / 2) (w ＞ 0) is π (1) the decreasing interval of the function (2) the function is in the interval [0,
F (x) can be reduced to f (x) = (1-cos2wx) / 2 + √ 3 sinwx coswx = - cos2wx / 2 + √ 3 / 2sin2wx + 1 / 2
By using the formula, we can get the above formula = sin (2wx - π / 6) + 1 / 2,
According to the meaning of the title, 2 π / 2W = π, so w = 1
So the decreasing interval of the function is. π / 2 + 2K π
How to calculate or make sin 20, cos 20, Tan 20 by geometric method
100% for those who can help me a lot
Sin20 = sin (30-10) = sin30cos10-cos30sin10 = 2sin10cos10, plus Sin & # 178; 10 + cos & # 178; 10 = 1, the results can be solved theoretically, and cos20 and tan20 will follow
If x = y and 2XY radical x + Y-1 is the arithmetic square root of X + Y-1, find the square root of X + y square
2XY radical x + Y-1 is the arithmetic square root of X + Y-1
The square of 2XY radical x + Y-1 is x + Y-1, that is 4x ^ 2Y ^ 2 = 1
X ^ 4 = 1 / 4 x + y square = 4x ^ 2 = 2
The square root of X + y square
±√2
The following functions are: ① y = - x, ② y = 2x, ③ y = - 1 / x, ④ y = x & # 178; (x < 0), the functions that y decreases with the increase of X are
The following functions are: (1) y = - x; (2) y = 2x; (3) y = - 1 / X; (4) y = x & # 178; (x < 0). The functions of Y decreasing with the increase of X are (1) (4)
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If the function y = logax has | y | > 1 on [2, + ∞), then the value range of real number a is ()
A. （12，1）∪（1，2）B. （0，12）∪（1，2）C. （1，2）D. （0，12）∪（2，+∞）
If a > 1, the function y = logax is an increasing function, the inequality | logax | 1 is log & nbsp; 1ax > 1. If 1 > a > 0, the function y = logax is a decreasing function, and the function y = Log & nbsp; 1ax & nbsp; is an increasing function, the inequality | logax | 1 is log & nbsp; 1ax > 1; In conclusion, the value range of real number a is (12,1) ∪ (1,2), so choose a
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How much is the 5 / 3 power of 3 multiplied by the 4 / 3 power of 3? Log with 1 / 3 as the base, logarithm of x = 4 / 3, x =?
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Log is based on 1 / 3, the logarithm of x = 4 / 3, the power of 3 / 4 of x = 1 / 3
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X is not on the denominator! X is on the numerator!
No~~
If the logarithm of three-quarters of log with a as the base is less than 1 (a is greater than 0, and a is not equal to 1), find the value range of real number a
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