# Square root of 2 cos2x: Mathway (2023)

Content

 1 Find exact value sin(30) 2 Find exact value sin(45) 3 Find exact value sin(30 deg. ) 4 Find exact value sin(60 deg. ) 5 Find exact value tan (30 degrees) 6 Find exact value arcsin(-1) 7 Find exact value sin(pi/6) 8 Find exact value cos(pi/4) 9 Find exact value sin(45 deg. ) 10 Find exact value sin(pi/3) 11 Find exact value arctan(-1) 12 Find exact value cos(45 deg. ) 13 Find exact value cos(30 deg. ) 14 Find exact value tan(60) 15 Find exact value csc(45 deg. ) 16 Find exact value tan (60 degrees) 17 Find exact value sec(30 grad. ) 18 Find exact value cos(60 deg. ) 19 Find exact value cos(150) 20 Find exact value sin(60) 21 Find exact value cos(pi/2) 22 Find exact value tan (45 degrees) 23 Find exact value arctan(- square root of 3) 24 Find exact value csc(60 deg. ) 25 Find exact value sec(45 grad. ) 26 Find exact value csc(30 deg. ) 27 Find exact value sin(0) 28 Find exact value sin(120) 29 Find exact value cos(90) 30 Convert from radians to degrees pi/3 31 Find exact value tan(30) 32 Convert from degrees to radians 45 33 Find exact value cos(45) 34 Simplify sin(theta)^2+cos(theta)^2 35 Convert from radians to degrees pi/6 36 Find exact value cot(30 grad. ) 37 Find exact value arccos(-1) 38 Find exact value arctan(0) 39 Find exact value cot(60 deg. ) 40 Convert from degrees to radians 30 41 Convert from radians to degrees (2pi)/3 42 Find exact value sin((5pi)/3) 43 Find exact value sin((3pi)/4) 44 Find exact value tan(pi/2) 45 Find exact value sin(300) 46 Find exact value cos(30) 47 Find exact value cos(60) 48 Find exact value cos(0) 49 Find exact value cos(135) 50 Find exact value cos((5pi)/3) 51 Find exact value cos(210) 52 Find exact value sec(60 grad. ) 53 Find exact value sin(300 deg. ) 54 Convert from degrees to radians 135 55 Convert from degrees to radians 150 56 Convert from radians to degrees (5pi)/6 57 Convert from radians to degrees (5pi)/3 58 Convert from degrees to radians 89 city. 59 Convert from degrees to radians 60 60 Find exact value sin(135 deg. ) 61 Find exact value sin(150) 62 Find exact value sin(240 deg. ) 63 Find exact value cot(45 deg. ) 64 Convert from radians to degrees (5pi)/4 65 Find exact value sin(225) 66 Find exact value sin(240) 67 Find exact value cos(150 deg. ) 68 Find exact value tan(45) 69 Calculate sin(30 deg. ) 70 Find exact value sec(0) 71 Find exact value cos((5pi)/6) 72 Find exact value csc(30) 73 Find exact value arcsin((square root of 2)/2) 74 Find exact value tan((5pi)/3) 75 Find exact value tan(0) 76 Calculate sin(60 deg. ) 77 Find exact value arctan(-( square root of 3)/3) 78 Convert from radians to degrees (3pi)/4 79 Find exact value sin((7pi)/4) 80 Find exact value arcsin(-1/2) 81 Find exact value sin((4pi)/3) 82 Find exact value csc(45) 83 Simplify arctan( square root of 3) 84 Find exact value sin(135) 85 Find exact value sin(105) 86 Find exact value sin(150 deg. ) 87 Find exact value sin((2pi)/3) 88 Find exact value tan((2pi)/3) 89 Convert from radians to degrees pi/4 90 Find exact value sin(pi/2) 91 Find exact value sec(45) 92 Find exact value cos((5pi)/4) 93 Find exact value cos((7pi)/6) 94 Find exact value arcsin(0) 95 Find exact value sin(120 deg. ) 96 Find exact value tan((7pi)/6) 97 Find exact value cos(270) 98 Find exact value sin((7pi)/6) 99 Find exact value arcsin(-( square root of 2)/2) 100 Convert from degrees to radians 88 city.

Final control in algebra and the beginnings of analysis

Teacher N.P. Gryzina MBOU School No. 3, Ozyory.

Boption 1. Part one.

1. Simplify the expression: (2sin2x – 2cos2x)tg2x

1. –cos2x. 2. 2. 3. – 4. 4. – 2sin2x

2.Find the value of the expression: 6tg2x - 2 if cos2x = 0.5

– 2. 2. – 5. 3. 22.4. 4.

3.Calculate: sin550 cos350 + cos550 sin350.

1. 1. 2.0. 3.Sin200. 4.— 2

4.Find the set of values ​​of the function y = 3cos28x - 2.

2.3.4.

5. Solve the equation: sinx - = 0

1.+2πn, nZ. 2. (- 1)n + , nZ

3.+n, nZ. 4.± +πn, nZ.

6.Solve inequality: ≥0

[2;+).2. (- ; — 4)

3.( — 4; — ] [2; +).4. (-;

7.The function is given by a graph on the interval . Indicate the values ​​of x for which the function is negative.

2. 3. (-1; 2). 4.[-4; -3) (-1; 2).

8.Find the derivative of the function y \u003d 4 × 3 - 2cosx

1. 12×2 + 2sinx. 2.12×3 + 2sinx. 3. 7×2 – 2sinx. 4.3×2 – 2cosx.

9.Specify an even function.

1. y=sinx – x2. 2. Y=x2 + x + cosx.3.Y=sin2x + x3.4. Y=7×2 +cos3x.

10. Find the slope of the tangent drawn to the graph of the function y \u003d x2 at the point with the abscissa x0 \u003d 1.

1.1. 2.2. 3. 3. 4. 0,5.

IN 1.Find the value of the expression: tg(π+α)sin( – α)cos( +α) for α=–

AT 2.The point moves in a straight line according to the law x(t) = 2t3 - 1.5t2 + 5 (where t is the time in seconds, x is the distance in meters). Calculate the speed of the point at time t = 2c.

B3.How many integers are in the scope of the function

F(x) = ?

Part two.

AT 4.The function is defined on the segment . The figure shows a graph of its derivative. Specify the number of minimum points of the function y = f(x).

B5.Find the longest interval of decreasing function

y= x3– 4×2 + 6x +3.

B6.Determine the number of roots of the equation 2sin2x - 3sinx - 2 = 0 on the segment.

AT 7.Find f(x0) if f(x) = (3x–5)2 + , x0= 2.

C1.Find the set of values ​​of the function f(x) = x+cos2x defined on the interval .

With 2. Find all solutions of the system of equations

satisfying the condition (x - y).

With 3.Find all values ​​of the parameter p for which the given equation has no roots:

4sin3x+3cos2x+p=0.

Option 2.

Part one.

A 1.Simplify the expression: sin22x.

1.–1.2.2. 3. 0. 4. 4.

A2. Find the value of the expression: 7 - 3cos2x if tg2x = 2. 1. 1.2.6.3. 5,5.4.4.

A 3. Calculate: cos 700 cos 200 - sin 700sin 200 .

1.–1. 2. Sin500. 3. Cos500. 4. 0.

A4. Find the set of values ​​of the function y = 6 + sin2x.

1. . 2..3. .4..

A5.Solve the equation: sin =.

1.(–1)n2. ±.3. (–1)n4.±

A6.Solve the inequality:

1.( –4;2][4;+).2.(–3. (–4.[–4;2]

A7.The function is given by a graph on the interval . Indicate those x values ​​for which the function is positive.

1.(–3;–1)2.(0;3].3.[–3;–1].4. (3;4).

A8. Find the derivative of a function: y= 6x4 - 3

1. 10x+3cosx. 2. 24×4– 3cosx. 3.24×3- 3cosx.4.4×3+3sinx.

A9.Specify an odd function.

1. y=x7+cosx. 2.Y=x5+2sinx.3. Y=2×3–cos2x.4.Y=x4+sinx.

A10.Find the slope of the tangent drawn to the graph of the function y \u003d 5x3–7x at the point with the abscissa x0 \u003d 2.

1.23. 2. 67. 3.8.4.53.

IN 1. Find the value of the expression: tgsin(2π-α)cos(π+α), with α=.

AT 2.The body moves in a straight line according to the law x(t)=3t3 - 2t2 - t (where t is the time in seconds, x is the distance in meters). Calculate the speed of the body at the moment t=2c.

B3.How many integers are in the scope of the function

F(x)=.

Part two.

AT 4.The function is defined on the interval [-5;3]. The figure shows a graph of its derivative. specify the number of maximum points of the function y=f(x).

B 5. Find the longest interval of increasing function

F(x)=–.

B 6. Determine the number of roots of the equation on a given interval:

2cos2x–5cosx+2=0, [0;π]. B 7. Find f'(x0) if f(x)=.

C 1. Find the set of values ​​of the function f(x)= x – , defined on the interval .

C 2. Find all solutions of the system of equations that satisfy the condition (x + y).

C 3. Find all values ​​of the parameter p for which this equation has at least one root pctg2x+2sinx+p=3.

Option 1.

Part one.

1.Represent the number - 0.125 as a square or cube.

A. (–0,25)2. B.(–0,5)3. IN. (–0,25)3.D. It is impossible to imagine.

2.Expressions are given: 1) ; 2) ; 3) Which of these expressions do not make sense at x=3?

A. only 2. B. only 1. IN.1 and 3. D.1 and 2.

3.Simplify the expression:

4.What is the value of the expression ?

A.

5.Solve an equation: 7x2+9x+2=0.

A. no roots. B.7; –2. IN. –1;. D. ; 1.

6.Find the value of an expression:

7.Solve the inequality: 5x+1

A.(–B.(2;+.IN. (–D.(–2;+

8.Solve the equation: x2+3x=0.

A.0;3. B. 0;–3.IN.0. D.–3.

9.Sort the numbers in ascending order.

10.Solve the system of inequalities:

11. Which of the following statements is true about the equation:

-3x2=2–x?

A.The equation has one root. B. The equation has no roots.

IN.has two roots of different signs. D. has two roots of the same sign.

12. For each graph, specify the function corresponding to it:

A) y=x2;B) u=–1.5x2; IN) y=-2x+2; D)in=

Part two. 1. (2 points) Solve the equation:

.

2.(4 points) Solve the system of inequalities:

3. (6 points) The boat travels 8 km upstream and another 30 km downstream in the same time it takes a raft to travel 4 km in this river. The speed of the boat in still water is 18 km/h. Find the speed of the river.

Option 2.

Part one.

1.Represent the number 0.0027 as a square or cube.

A.(0,09)2. B.0,33. IN.(0,03)2. D.It is impossible to imagine.

2. Expressions are given: 1) ; 2) Which of these expressions do not make sense at x=-3.

A.Only 1. B. 1 and 2. IN. 2 and 3.D.1 and 3. 3.Simplify the expression:

4.What is the value of the expression ?

A.. B.. IN. –25. D.25.

5.Solve the equation: 5x2–7x+2=0.

A.1,6; –. B. 1; .IN. –1;–0,4.D.There are no roots.

6.What is the value of the expression

7. Solve the inequality: 2x + 5.

A. (–B.(–IN.(–1;+D. (4;+

8.Solve the equation: x2-9x=0.

A.–9. B.0; 9. IN.0.D. 0;–9.

9.Arrange the numbers 2.5; and in ascending order.

10. Solve the system of inequalities:

11. Which of the following statements is correct regarding the equation 3x2=4-x?

A.The equation has a single positive root.

B.The equation has a single negative root.

IN.The equation has two roots of different signs.

D.The equation has two roots of the same sign.

12. For each graph, specify the function corresponding to it.

A.u=1.5x2;B. in=; IN.Y=2x; D.Y=-x3;

Part two.

1. (2 points) Solve the equation: – =.

2. (4 points) Solve the system of equations:

3. (6 points) The motorcyclist covered the distance from point M to point N in 5 hours. On the way back, he rode the first 36 km at the same speed, and the rest of the way at a speed of 3 km/h more. At what speed did the motorcyclist initially drive if he spent 15 minutes less on the way back than on the way from M to N?

## sinx + cosx = sqrt(2) cos2x

CHHAYA PUBLICATION - GENERAL SOLUTIONS OF TRIGNOMETRIC EQUATIONS - Short Answer Questions

20 videos

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Updated on: 27-06-2022

Text solution

Nπ-π4,2nπ+π12,2nπ-7π12

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11. sin theta +sin 2theta+sin3theta+sin4theta=0 92x_1`

`sinx_1=sqrt(2)`

If you try to calculate `arcsinsqrt2` in your calculator, you will get an error. This is because it doesn't exist. The values ​​that exist for arcsin range from -1 to 1, and `sqrt(2)>1`

The value of `sin((3pi)/4)` is `sqrt(2)/2`; hence it cannot be a solution for `arcsinsqrt2` . Rather, it is the product of one existing root `pi/4`.

Also note in the graph of the function that the graph does not intersect the x-axis at sqrt(2), further confirming that the root does not exist. Rather, all roots of this function are multiples of 1 existing root, pi/4, since this is an infinitely repeating function. 92x_2`

Because you can't take the square root of a negative number, x2 doesn't exist. Startwith 48 hour free trialto access over 30,000 additional tutorials and over 350,000 homework help questions answered by our experts.

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