![](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>)
After y = SiNx (2x + π / 4) image translation vector (π / 4,0), the function corresponding to the new image is y=
The vector (π / 4,0) is to shift π / 4 units to the right, which is equivalent to changing y = f (x) into y = f (x - π / 4)
So, after translation
y=sin[2(x－π/4)＋π/4]
=sin(2x－π/4)
After the image of function y = SiNx is translated by vector a = (- π / 4,2), it coincides with the image of function g (x), and the expression of G (x) is obtained
Translation by vector a = (- π / 4,2)
That is, shift π / 4 to the left and 2 to the upper
y=sin(x+π/4)+2
g（x）=sin(x+π/4)+2
Add: vector translation is not based on plus or minus signs
As in this question, - π / 4 is on the left of the axis
So it's a left shift
Let f (x) = cosx SiNx, translate the function image of F (x) according to vector a = (m, 0) (M > 0), and get the image of function y = - f '(x) Then the value of M can be?
(x) = cosx-sinx = 2 (x = 2 / 2cosx - √ 2 / 2 / 2sinx) = √ 2 (COS π / 4cosx-sin π / 4sinx) = √ 2cos (x + π / 4) f '(x) = - √ 2Sin (x + π / 4) y = - f' (x) = √ 2Sin (x + π / 4) y = - f '(x) = √ 2Sin (x + π / 4) √ 2cos (x + π / 4) → right translation (π / 2 + 2K π) units to get → √ 2Sin (x + X + X + x + 2 + 2K π π π π) units get → √ 2Sin (x + X + X + X + X π / 4) (M > 0), so m =
After the image of function f (x) = cosx (x ∈ R) is translated by vector (m, 0), the image of function y = SiNx is obtained, then the value of M is a x=π/2 b=π c=-π d=-π/2 Explain in detail!
Let f (x) = cosx be (x, y), and then translate it into (x ', y') according to vector (m, 0)
That is: x + M = x ', y + 0 = y'
So we have: F (x) = y '= cosx = cos (x' - M), and y '= SiNx'
That is, SiN x '='
So, M = π / 2
If the image of the function f (x) = SiNx is vector A = (- π, − 2) is translated to get the image of function g (x) (1) Find the analytic expression of function g (x); (2) Find the function f (x) = f (x) - 1 The minimum value of G (x)
(1) Let P (x, y) be any point on the image of function f (x) = SiNx, and the corresponding point on the image of function g (x) after translation by vector a = (- π, - 2) is p '(x', y '), then x' = x − π y ′ = y − 2} x = x ′ + π y = y ′ + 2, that is y ′ + 2 = sin (x ′ + π)
The image f of the function f (x) = (2 √ 3cosx SiNx) -√ 3-2 is translated into f by vector a. the analytic formula of F 'is y = f (x). When y = f (x) is an odd function, vector a can be equal to () A.（π/6,-2) B.(π/6,2) C(-π/6,-2) D(-π/6,2) I'm sorry, the question is wrong It is a function that translates the image f of the function f (x) = 2cosx (√ 3cosx SiNx) -√ 3-2 according to vector a. the analytic formula of F 'is y = f (x). When y = f (x) is an odd function, vector a can be equal to () A.（π/6,-2) B.(π/6,2) C(-π/6,-2) D(-π/6,2) But the answer is d
The image f of the function f (x) = 2cosx (√ 3cosx SiNx) -√ 3-2 is translated into f by vector a, and the function analytic formula of F 'is y = f (x). When y = f (x) is an odd function, vector a can be equal to () a. (π / 6, - 2) B. (π / 6,2) C (- π / 6, - 2) d (- π / 6,2) analytic: ∵ function f (x) = 2cosx (√ 3cosx sin
Solving a trigonometric function calculation problem If Tan (α + β) = 2 / 5, Tan (β - π / 4) = 1 / 4, then cos α + sin β is higher than cos α - sin β =?
Tan [α + β (β - β - π / 4)] = Tan [α + β (β - π / 4)] = Tan (α + β + β (β - π / 4) / [1-tan (α + β) Tan (β - π / 4 / 4)] will replace Tan (α + β) = 2 / 5tan (β - π / 4) = 1 / 4 into the original formula = Tan (α + β) + Tan (β - π / 4) / [1-tan (α + β) Tan (β - π / 4)] = (2 / 5 + 1 / 4) / (1 / 5 + 1 / 4) / (1 / 5 + 1 / 4) / (1 / 1 / 4) / (1 / 5 + 1 / 4) / (1 / 1 / 1 / 1 / 4) / (1 / 5 + 1 / 4) / - 2 / 5 * 1 / 4) = 1
Help me solve a trigonometric function problem There is an observation point a on the island. At 11:00 a.m., a ship was measured at 60 degrees north by east of the island and 50 N miles away from the island. 2 hours later, the ship was measured at 60 degrees north by west of the island, 30 n miles from the island (1) Find out the speed of the ship (the ship runs in a straight line, (2) If the course does not change, when will the ship arrive due west of the island?
Let the ship speed be 35n miles / h only considering the North-South distance and zero when it is due West: the initial north-south distance is 50N mile * cos60 = 25N mile2h, and then the North-South distance is 30n mile * cos60 = 15N
Difficult problem of trigonometric function in senior one Sin α + sin β = 1 / 3, find the maximum value of sin α - (COS β) ^ 2
Sin α + sin β = 1 / 3 find the maximum value of sin α - (COS β) ^ 2
sina=1/3-sinb
(cosb)^2=1-(sinb)^2
So Sina - (CoSb) ^ 2
=1/3-sinb-[1-(sinb)^2]
=(sinb)^2-sinb-2/3
=(sinb-1/2)^2-1/4-2/3
=(sinb-1/2)^2-11/12
Because Sina + SINB = 1 / 3
Sina = - 2 / 3
When SINB = - 2 / 3
(sinb-1 / 2) ^ 2 has a maximum
So the maximum is
(-2/3-1/2)^2-11/12
=4/9
sin15°−cos15° sin15°+cos15°=______ .
Divide the numerator and denominator of the original formula by cos15 °,
There are sin15 ° - cos15 °
sin15°+cos15°=tan15°−1
tan15°+1=tan15°−tan45°
tan15°tan45°+1
=tan（15°-45°）
=tan（-30°）=-
Three
3．
So the answer is: --
Three
Three
RELATED INFORMATIONS
- 1. How to find tangent equation of curve at a certain point according to the geometric meaning of derivative
- 2. Exercises on extremum and derivative of function 1. Find the extremum of the following functions （2）y=48x-x^3 （3）y=6+12x-x^3 （4）y=5x+x^3 （5）y=x^2-7x+6 （6）y=x-x^3 5. It is known that f (x) = ax ^ 3 + BX ^ 2 + CX (a ≠ 0) has an extreme value when x = ± 1, and f (1) = - 1, (1) Try to find the values of constants a, B and C (2) Try to judge whether the function gets minimum or maximum when x = ± 1, and explain the reason 6. Let f (x) = x ^ 3-3ax + B (a ≠ 0) (1) If the curve y = f (x) is tangent to the straight line y = 8 at the point (2, f (x)), find the values of a and B; (2) Find the monotone interval and extreme point of function f (x) 7. Let y = f (x) be a cubic function and the image is symmetric about the origin. When x = 1 / 2, the minimum value of F (x) is - 1, and the analytic formula of function f (x) is obtained 8. F (x) = x ^ 3 + 3ax ^ 2 + BX + A ^ 2 has an extreme value of 0 when x = - 1 (1) Find the values of constants A and B; (2) Find: monotone interval of F (x) Don't talk if you don't answer!
- 3. The equation of conic curve. Find the hyperbolic equation with two vertices of ellipse x squared / 16 + y squared / 9 = 1 as focus and ellipse focus as vertex
- 4. The problem of finding tangent by derivative If the function y = f (x) passes through the tangent line of point P (x, f (x)), there are two cases, one is that the point is tangent point, the other is that the point is not tangent point, so there may be two answers My question is, isn't the tangent line only one intersection point with the image of y = f (x)? Since the point P (x, f (x)) is on y = f (x), isn't p the tangent point? If not, isn't the tangent point more than one intersection point with the image of y = f (x)?
- 5. In the triangular vertebrae with o as the vertex, the intersection angle of the three edges passing through O is 30 degrees. Take two points AB on one edge, OA = 4cm, OB = 3cm. At the end point of AB, a rope is used to tightly wrap the side of the triangular pyramid (there is no friction between the rope and the side), and find the shortest rope length between AB and ab
- 6. Can we prove that the line m is perpendicular to the line n?
- 7. The derivative of the function y = sin2x - cos2x is () A. 2 2cos(2x-π 4) B. cos2x-sin2x C. sin2x+cos2x D. 2 2cos(2x+π 4)
- 8. Y = x to the third power, derivative over Y?
- 9. A derivative calculation, Y equals V times the square of u, V equals x plus 2A. U equals x minus A. I know how to divide them into several functions and how to calculate them?
- 10. Given that sina = three quarters, cos (a + b) = minus two thirds, a, B are acute angles, find SINB
- 11. Find the solution set of the inequality system 1.2x-75 3x-2≥4 3.1-2（1+y)-3/4 x≥5
- 12. In the inequalities with unknowns, () is called inequality solution of inequality
- 13. What is the concept of inequality?
- 14. What is the solution formula of quadratic inequality of one variable Isn't the result of two values? It doesn't become to understand the quadratic equation of one variable
- 15. How to solve the inequality with absolute value? For example: | 1-3x | 4 problem solving process, as long as detailed steps, don't say a lot, I think we all understand a kind of problem do not understand, as long as you look at the problem-solving process can roughly understand it? So don't copy some theories to send up! At present, just read senior one, senior one solution priority, other night can!
- 16. Solving inequality: 1 + SiNx + cosx ≠ 0
- 17. The graph of the function y = - 3x + 12 is drawn, and the solution set of inequality - 3x + 12 > 0 is obtained by using the image. (2) the solution set of inequality - 3x + 12 ≤ 0 is obtained
- 18. Using function image to solve inequality 5x-1 > 2x + 5
- 19. What is the area of the plane area represented by the absolute value of inequality x + absolute value y less than or equal to 3
- 20. Try to determine the value range of a, so that the inequality group x+x+1 4＞1 1.5a−1 2(x+1)＞1 2 (a − x) + 0.5 (2x − 1) has only one integer solution