7. In Cape Capstan, low tide of 2m occurs a 5:00am and a high tide of 10m occurs at 11:00am a) Find a cos function to represent the height of the tide in metres at time t in hours. (24 hour clock and t=0 is midnight) b) Find a sin function to represent the height of the tide in metres at time t in hours. (24 hour clock and t=0 is midnight) c) Determine the height of the tide at 2:00pm. d) Determine the time(s) when the tide will be 4m deep in one 24 hour period. (midnight to midnight)

Q: for the equation 8x(x−1) +cos(x) =0 does the intermediate value theorem show at least one solution…

A: Let, f(x)=8x(x−1) +cos(x) 8x(x−1) and cos(x) both are continuous for all real values of x. So, f(x)…

Q: Q4:B/Simplify [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's theorem?

A:

Q: 18. Use periodicity to express sec in p given that sin

A:

Q: 5. Given that 2 sin 20 = cos 20, a) show that tan 20 = 0.5. b) hence find the values of 0, to one…

A: given that 2sin2θ=cos2θ to prove that tan2θ=0.5 proceed as follows  2sin2θcos2θ=1tan2θ=12tan2θ=0.5

Q: 1. Find the exact values of sinh (0) and cosh (0) using their definitions.

A: Sinh x=ex-e-x2∴ sinh0=e0-e-02=1-12=0∴sinh0=0      cashx=ex+e-x2∴cash0=e0+e-02=1+12=1⇒cash0=1

Q: find the four non zero terms in the maclaurin serise for sin h-lx

A: Formula Used: We will need following binomial expansion:

Q: 3. Express 1+cos2x in terms of cos x. hence a. Evaluate (1 + cosx)dx b. Express 1- cos2x in terms of…

A:

Q: 9. Find the other trigonometric functions of 0 of sec 0 3 and 0 does not terminate

A:

Q: 8. Show that sin a (1+ tan a) + cos a (1 + cot a) = sec a + csc a.

A:

Q: To four decimal places , find all solutions for Cos X = 8.

A: To find the solution of the given trigonometric equation.

Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

Q: 1. Use the Intermediate Value Theorem to show that there is the solution to the equation cos(x)=x in…

A: Given cosx=x

Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

A:

Q: the action of a spring can be modeled by the function y=4 cos x- cos x sin x after x seconds  Within…

A: To find the height at which spring has height of 3 feet

Q: Obtain graphically an approximate value of the lowest root of cos x cosh x =- 1.

A: The equation cosxcoshx=-1 regulates the frequency of vibration of a cantilever. We must first…

Q: If cos A %3D with A in QII V10 Find tan 2A. HIN

A:

Q: 4 5 Points ntegral of sin-cos-sin0 de has the form (e) +C. What should be the value of e =0?

A:

Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

A:

Q: If z =7 tan 0, express sin (20) as a function of z. sin (20) =

A:

Q: Given that sin-(x) = a and cos-(x) = B show that sin(a + B) = 1. %3D

A:

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

A:

Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin x tan 2. Given the…

A: We can solve the given problem as follows:

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: Express f (0) = cos 20 + 4(sin 20)² + 1 as a sum of powers of sin 0.

A:

Q: Show that cos bx = (eibx +e-ibx) and 1 sin bx :(eibx – e-ibx). 2i

A:

Q: At what points do the local and absolute extreme values of the function (x) = 2 cos x- x^2 occur on…

A: We have to solve given problem:

Q: 2. Suppose tan x = 3 -- with < x < 2n. Find the exact value of cos ). Show you work carefully. ensem…

A: Given problem:- tan(x) =-4/3 with 3π/2 &lt;x&lt; π To find:- Exact value of cosx2)

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

A:

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40³[cos 20-i sin2015 using De…

A: Formula Used-  De Moivre's theorem: cosθ+isinθn=cos nθ+isin nθ cos mθ+isin mθcos nθ+isin nθ=cos…

Q: 05 of the ac 42. Use the identity sin 2x = 2 sin x cos x to find the derivative of sin 2.x. Then use…

A: Find the derivative sin2x

Q: 5) prove that = sin 'x +e using method of trigonometric substitution.

A: To Prove- Prove that ∫dx1 - x2 = sin-1x + c using method of trigonometric substitution.

Q: 16. Consider a projectile launched from ground level at an angle of elevation 0 with an initial…

A:

Q: 4. Use Walli's formula to evaluate 2 sin*x cos°xdx.

A: Given integral is as below:-                  ∫0π2 sin4xcos9xdx

Q: Can the Intermediate Value Theorem be used to prove that the equation 9 2(r + 9) sin*(x) – 4 cos"(x)…

A:

Q: 11.Show that A cos (ω0t) + B sin (ω0t) can be written in the form r sin(ω0t − θ). Determine r and θ…

A:

Q: 9 Suppose that a cos x = 1 + sin x, where 0° < x < 90°. a a Prove that 1 = t, where t = tan x. a + 1…

A:

Q: 3. When e is in standard position and its terminal side passes through the point (4, -2) Find the…

A: Given: θ is in standard position and its terminal side passes through point (4,-2)

Q: When a pendulum 0.5 m long swings back and forth, its angular displacement O from rest position, in…

A: Given    Diagram we have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the…

Q: An electric current can be represented by the function y=2 cos (2 here is the character that looks…

A: An electric current can be represented by the function y=2 cos (2 here is the character that looks…

Q: 33. Use addition formulas and the values of sin 0 and cos 0 for 0 = to compute sin 12 and cos…

A: Given: sin7π12, cos7π12 We know that sinA+B=sinAcosB+cosAsinB…

Q: The range of this Y= 2 cos (3x) Is?

A:

Q: A series RLC circuit has a hypothetical current that is described by the expression, 1(t) = 6e-¹ sin…

A:

Q: Suppose that 3π/2≤θ≤2π,  csc(θ)=11/4, find sin(θ)=______. (round to 3 decimal places)

A:

Q: Assume sin(0) = 12 where 0 < 0 <. Compute the following in terms of x. tan (20) cos (2) - -

A:

Q: Q6 (i) Show that sin 20(tan 0+ cot0) = 2. (ii) Hence (a) find the exact value of tan+tan+cot+cot,…

A: see below the calculation and answer

Q: Suppose that π/2≤θ≤π, sin(θ)=2/9, find cos(θ)=______. (round to 3 decimal places)

A: Here, θ is in the second quadrant( π/2≤θ≤π) and cosine is negative in the second quadrant.