![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given the square X-1 of the function f (x) = sin (2x + 60 °) + sin (2x-60 °) + 2cos, X belongs to R. find the minimum positive period of the function FX, and find the maximum and minimum value of the function FX in the interval [- 45 ° 45 °]
F (x) = sin (2x + 60 °) + sin (2x-60 °) + 2cos squared X-1, f (x) = 2Sin (2x) cos60 + cos2x = sin2x + cos2x = Radix 2 (sin2x + 45), so the minimum positive period is Wu. - 45
Let f (x) = cos (x + 2 π of 3) + π of 2cos square, X belongs to R, and find the value range of F (x)
f（x）=cos（x+2π/3）+2cos²π/2=cos（x+2π/3）+2*0=cos（x+2π/3）
∵－1≤cos（x+2π/3）≤1
The value range of the function is 〔 - 1,1]
The function f (x) = SiNx cos (x + π) 6) The value range of is () A. [-2，2] B. [- 3， 3] C. [-1，1] D. [- Three 2， Three 2]
The function f (x) = SiNx cos (x + π)
6）=sinx-
Three
2cosx+1
2sinx
= -
Three
2cosx+3
2sinx
=
3sin（x-π
6）∈[−
3，
3]．
Therefore, B
Given the function y = - SiNx cos square x, find the value range
sin^2 x+cos^2 x=1
So y = - SiNx cos ^ 2x = - sinx-1 + sin ^ 2 x = sin ^ 2 x-sinx-1
Let a = SiNx
Then - 1 ≤ a ≤ 1
y=a^2-a-1=(a-1/2)^2-5/4
So a = 1 / 2, y min = - 5 / 4
So a = - 1, y max = 1
So the range is [- 5 / 4,1]
The function f (x) = SiNx cos (x + π) 6) The value range of is () A. [-2，2] B. [- 3， 3] C. [-1，1] D. [- Three 2， Three 2]
The function f (x) = SiNx cos (x + π)
6）=sinx-
Three
2cosx+1
2sinx
= -
Three
2cosx+3
2sinx
=
3sin（x-π
6）∈[−
3，
3]．
Therefore, B
Given the function f (x) = 2cos (x + π / 4) cos (x - π / 4) + √ 3sin2x (1), find the minimum positive period (2) of function f (x) if 0
The function can be reduced to f (x) = 2Sin (2x + π / 6), period π and range (- 1,2)
The value range of the function f (x) = 2cos (x + π / 4) cos (x - π / 4) + 3sinx is obtained
F (x) = 2cos (x + π / 4) cos (x - π / 4) + 3sinx = cos (2x) + cos π / 2 + √ 3sinx = 1-2sin? X + √ 3sinx = - 2 (sin? X - √ 3 / 2sinx) + 1 = - 2 (SiNx - √ 3 / 4)? + 11 / 8
The value range of the function y = | cos X - 2cos x is
When cosx ≥ 0, y = cosx-2cosx = - cosx, y ∈ [- 1,0]
cosx
It is known that the odd function f (x) is defined on (- ∞, 0) ∪ (0, + ∞), and is an increasing function on (0, + ∞), f (1) = 0; the function g (θ) = sin2 θ + m · cos It is known that the odd function f (x) is defined on (- ∞, 0) ∪ (0, + ∞), and is an increasing function on (0, + ∞), f (1) = 0; the function g (θ) = sin2, θ + m · cos θ - 2m, θ∈ [0, π / 2]. If the set M = {m| g (θ)
Is the set n = {m| f [g (θ) < 0]} wrong, should be n = {m| f [g (θ)] < 0}?
The minimum positive period of the function f (x) = sin2 π x + cos ^ 2 π x is
f(x)=sin2πx+cos^2πx
=sin2πx+[cos2πx+1]/2
=sin2πx+1/2cos2πx+1/2
Because the minimum positive period of sin2 π X and Cos2 π x is π
Therefore, the minimum positive period of F (x) is π
RELATED INFORMATIONS
- 1. Given that the angle α is an acute angle and sin2 α - sin α cos α - 2cos α = 0, find the value of Tan α Sorry, here sin2 α is the square of sin α, 2cos α, because it should be 2 times the square of cos α
- 2. It is known that f (x) = 2Sin (x + θ / 2) cos (x + θ / 2) + 2 √ 3cos ^ 2 (x + θ / 2) -√ 3 Question: if 0 ≤ θ ≤ π, and the function f (x) is even, find the set of X satisfying the equation f (x) = 1 and X ∈ [0, π] The answer is x = 5 π / 6 or x = π / 6 I just can't figure out pi / 6
- 3. It is proved that Tan (3a / 2) - Tan (A / 2) = [2Sin (A / 2)] / [cos (3a / 2)]
- 4. If f (x) = 2tanx + 2sin2x 2−1 sinx 2cosx 2, then f (π) 12) The value of is______ .
- 5. In the triangle ABC, if sin (2 π - a) = - radical 2 (π - b) and root 3cosa = - radical 2cos (π - b), find the three inner angles of triangle ABC
- 6. F (x) = - sin2x + 2 times root sign 3sin? X - radical sign 3 + 1, find the minimum positive period and the simple decreasing interval
- 7. Given the vector a = (2cosx / 2, Tan (x / 2 + π / 4)), B = (√ 2Sin (x / 2 + π / 4), Tan (x / 2 - π / 4)), Let f (x) = vector a * vector B, find the range of value of F (x), the minimum positive period
- 8. The known function f (x) satisfies f (TaNx) = 1 Sin2x · cos2x, find the analytic formula of F (x)
- 9. Given that the minimum positive period of the function y = 1 / 2Sin [(x + π) / a] (a > 0) is 3 π, then a =, the value range of the function is:
- 10. The minimum positive period and monotone decreasing interval of function f (x) are obtained by given the function f (x) = cos? X-sin? X + 2 √ 3sinxcosx + 1 (1) (2) When x ∈ [- 6 / π, 3 / π], f (x) - 3 ≥ m holds. Try to determine the value range of M
- 11. How is pi found and calculated?
- 12. What is Pi? How does PI come from?
- 13. Why does the calculator multiply 3.1415926 by 3.1415926 and divide by 3.1415926 is 3.1415925?
- 14. Accurate value of PI The more, the better!
- 15. Find the monotone increasing interval of the function y = sin (1 / 2x + π / 3), X ∈ [- 2 π, 2 π]
- 16. The function y = sin (- 2x + π) 4) The monotone increasing interval of is___ .
- 17. Find the monotone increasing interval and monotone decreasing interval of sin (2x + π - 4) at the bottom of function y = log2
- 18. Trigonometric function FX = 2 √ 3cos ^ 2 + 2sinxcosx-m, in the interval [0] Trigonometric function function FX = 2 √ 3cos ^ 2 + 2sinxcosx-m, on the interval [0, π / 2], the maximum value of the function is 2, and find the value of M. in △ ABC, the opposite side of angle ABC is ABC. If a is an acute angle and satisfies FA = 0, SINB = 3sinc, △ ABC area is 3 √ 3 / 4, find the side length a
- 19. Given the square (x / 2) + sinx-1 of function FX = 2cos, find the minimum positive period sum range of function FX The square (x / 2) + sinx-1 of the known function FX = 2cos Finding the minimum positive period sum range of function FX If x belongs to [π / 2,3 π / 4], and FX = 1 / 5, find the value of SiNx
- 20. If x belongs to (0, π) and SiNx + cosx = - 1 / 5, then cos2x