Find the specified quantity. Explain the vertical translation. Find the vertical translation of \( y = -2 + \sin \left( 3x + \frac{\pi}{6} \right) \).

Q: Show that x = 2 +3i is a solution to the equation x2 - 4x + 13 = 0.

A:

Q: Prove that each of the following identities is true.     tan theta cosec theta cos theta = 1

A:

Q: Convert -390 degree  to radian measure. Write your answer as an exact value.

A:

Q: Use addition of y-coordinates to sketch the graph of each of the following between x =0and x = 4p.  ...

A: Given: y=13x-cosx,   0≤x≤4π

Q: Determine an appropriate viewing rectangle for each function, and use it to draw the graph. = tan 25...

A: Given: y=tan 25x To Determine: An appropriate viewing rectangle for the given function. Graph the gi...

Q: Area of a Sector A central angle of 2 radians cuts off an arc of length 12 inches.Find the area of t...

A: Given: Central angle of sector of a circle =2 radians Length of arc=12 inches We know that if centra...

Q: Find all solutions to the following triangle. (Round your answers for the angles B, C, B', and C' to...

A: A=63°, b=6.7yd, a=6.2 yd

Q: To estimate the height of a tree, one person stands due north of the tree and a secondperson stands ...

A: As the distance between the tree and the two people are equal thus let the distance between the tree...

Q: For each equation, find all degree solutions in the interval 0° <= u < 360°. If rounding isnec...

A: Given that 16cos2u-18sin2u=0

Q: 2. Write the domain and range and determine whether the relationship given in the mapping is a funct...

A: According to the question, we have to write the domain and range of the relation and check that whet...

Q: If z = os0+ I sin 0 and y= cos Isin p, then show that %3D 2 cos(@-).

A:

Q: 4. Determine the sign (+ or -) a. cos 143 degree, b. tan 192 degree. c. tna (4 pi/5)

A:

Q: Identify the horizontal translation for each equation. Do not sketch the graph.          y = cos  ( ...

A: To Determine: Identify the horizontal translation for each equation. Do not sketch the graph. Given:...

Q: Show all steps

A: 6 tan2x + 13 tanx - 5 = 0       on  x ∈ [0, 2π)=>  6 tan2x + 13 tanx - 5 = 0=> 6 tan2x + 15 ta...

Q: Which statement is possible for some real number z ?       sin z =2

A: Given: sin z =2

Q: Prove the following identities.    cos 4 theta  = 1/ 4 +cos  2 theta / 2 + cos 2  2 theta / 4

A: To prove the given identity.

Q: Trigonometry Question

A: Given:   sinθ cosθ secθ cotθReciprocal Identities:secθ=1cosθtanθ=sinθcosθcotθ=1tanθ=cosθsinθ

Q: 71-78 · Even and Odd Functions Determine whether the func- tion is even, odd, or neither. (See page ...

A: The given function is f(x)=x2sinx   known fact: A function f is even if and only if f-x=fx for every...

Q: Find sin(-theta)

A: Given,     sin θ  = -18

Q: Find all exact solutions on [0, 27). (Enter your answers as a comma-separated list.) 2 sin(40) = V2 ...

A: Since you have asked multiple questions in single request  so we  will be answering only first quest...

Q: Use a calculator to find each of the following. Round all answers to four places past thedecimal poi...

A: Concept:   The trigonometric ratio are ratios, sine, cosine, tangent, cosecant, secant and cotangent...

Q: Write each of the following in terms of sin theta and cos theta; then simplify if possible.   sin th...

A:

Q: Show that each of the following is true. cos (180 degree - theta ) = - cos theta

A: cos(180°-θ)=-cosθ

Q: Sketch the graph from x = 0 to x = 4p.       y = sin  x - cos x

A: Given function y=sinx-cosx.  

Q: Simplify the absolute value in 2 )sin u) if u = cos- 1 x/2for some real number x.

A:

Q: Use the given information and a calculator to find theta to the nearest tenth of a degree if0 degree...

A: cot theta = -0.7366                0 degree < =theta   < 360 degree cot θ = -0.7366           ...

Q: In a right angled triangle, the area of thesquare on the hypotenuse is the sum of theareas of the sq...

A: In a right angled triangle, the area of the square on the hypotenuse is the sum of the areas of the ...

Q: Convert to polar coordinates.    (3, 3)

A: Given coordinate is 3,3. We have to convert given coordinate into polar coordinate. In Polar form co...

Q: 8. Find sec (30 deg), csc (225 deg),

A:

Q: Graph the equation r = 2 cos 2u + 3 sin u using your graphing calculator in polarmode.

A: The given equation is r=2cos2u+3sinu. Sketch the graph of the equation as shown below.  

Q: Pac-Man Figure 17 shows an image of Pac-Man from the classic video game.The “mouth” of Pac-Man forms...

A: Given angle of open mouth 55o radius= 4mm

Q: Find the area of the sector formed by the given central angle theta in a circle of radius r

A: Area of sector is given by:

Q: Graph one complete cycle of each of the following. In each case, label the axes accurately.   y = 1/...

A: To Determine: Graph one complete cycle of each of the following. In each case, label the axes accura...

Q: State the formula for a circle with center (h, k) and radius r.

A: A circle is the set of all the points that are at a distance of r (called as radius) from the point ...

Q: Evaluate without using a calculator.     sin    -1 ( sin pi/6)

A:

Q: Indicate the two quadrants  could terminate in given the value of the trigonometricfunction. sin th...

A: For 180°<θ<0° that is first/second quadrants then sin θ has a positive value. For 180°<θ&lt...

Q: When simplifying radical expressions, it is necessary to write any square root of a_______ number in...

A: The given statement is  When simplifying radical expressions, it is necessary to write any square ro...

Q: Change r2 =9 sin 2u to rectangular coordinates.

A: given: r2=9sin2u we have to change it into rectangular coordinates. as we know that in rectangular c...

Q: Let f(x) = 2x - 5 and g(x) = x2 +3x + 4. Evaluate the following.         g (2b)

A: Given functions are fx=2x-5 and gx=x2+3x+4. We have to evaluate g2b. Put x=2b in the gx, we get g2b=...

Q: Arc Length Find the length of arc cut off by a central angle of p/6 radians in a circleof radius 10 ...

A: Given central angle of a circle=π6 radian. Radius of circle=10 cm We have to find length of arc cut ...

Q: If sin  B  = -1/3 with A ,find the following  sin B/2

A: Given: sinB=-13 we know that sinx is negative in third and fourth quadrant now if sinB in third quad...

Q: In general, round answers so that the number of significant digits in your answermatches the number ...

A: Concept: The trigonometric ratio are ratios, sine, cosine, tangent, cosecant, secant and cotangent. ...

Q: Solution please

A: Given that: A river flows next to a cliff on one side and has a wide flat plain on the other. At the...

Q: Graph one complete cycle of y = 1/2 sin 3x. State the amplitude and period.

A: Graph of y=12 sin3x. Also to determine amplitude & period.