Evaluate the trig function by drawing the appropriate triangle.  1. tan(π/3) 2. cos(7π/6) 3. sin(5π/3)

Q: VI. Use the given information to find the exact function values. a) sin (a/2) b) cos (a/2) c) tan…

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Q: Given: tan0 = and 0<0< 3 %3D Find the exact value of: sin- V14 A) top hats B) 4 suspenders V14 C) 4…

A: Given, tanθ=73 and 0≤θ≤π2

Q: Using trigonometric substitutions, S Vx2-9 dx , x > 3, is equal to: 3x

A: Given:            ∫x2-93xdxwe know that trignomentric equationsec2θ-tan2θ=1Here substitute x=3secθ…

Q: 5) Use the trigonometric substitution to write the algebraic expression as a trigonometric function…

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Q: 4x? )(i) Use the substitution x= tan e to show that sin? 20 dx. %3D (1+x*)' 4x2 (ii) Hence find in…

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Q: dx =+ v3- 2. Determine the value of k such that sin 6

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Q: 7V3 14 Y 8) What is the measurement of segment ZY? 9) What is sin X of the triangle? 10) What is cos…

A: our objective is to find ZY, Sin X,Cos X

Q: How can we find x using SohCahToa? sin 34 = %3D y cos 34 = tan 34 = 34°

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Q: = - In(- cost) – e sinr, find the value of y' when t= 4 If "y=sin?t+ tant, x=

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Q: 4 Using trigonometric substitutions, S dx is equal to: xV16 – x²

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Q: c. At what time does each vibration first reach a displacement of –2mm? d. Use the compound angle…

A: 1) x1=3.75sin100πt+2π9     x1=3.75(sin100πtcos2π9+cos100πtsin2π9)     x1=Asin100πt+Bcos100πt…

Q: The modified EuleriMethad Use to solue Sined y at x= 0.1 h=o.02

A: Given differential equation is y'=x+y, y(0)=1. To find the value of the solution at x=0.1 using…

Q: What is the value of b that will result in a period of 90° for y =a sinb(x-c) +d? (A) (B) (C) 2 (D)…

A: Period of the transformation

Q: etion) 16 sin? (4/7) cos³ (2VI)

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Q: - 25 csce A <0 < Given that 24 where 2 , find the exact value of the trig function using the half…

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Q: 45 F 28 53 What is the sin D of the triangle above? What is the sin E of the triangle above?

A: Given, A right angle triangle DEF with sides  DF = 45DE = 53EF = 28  We have to find the value of…

Q: Q1/ Find L{sin(at + b)}

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Q: 12. Explain why using trigonometric substitution with x = a tan u often involves a triangle with…

A: Consider the right triangle below with angle u , opposite side x and adjacent side a.

Q: 12. In the right triangle shown, find the sin a . B) vx-1 C) vi-x A) x D) I-x

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Q: a) Which trigonometric substitution needed V25 – x2 dx ? to be used to solve Answer: x = sin 0 b)…

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Q: C Match the trig function with the correct ratio. 4 sin A = cos A = tan A = 3

A: Correct ratio

Q: 1) What is the ratio of the sin X? 4 Y X 4/5 3.

A: Sinx =  ZY/ZX Sinx = 4/5

Q: Use the unit circle to find all values of 0 between 0 and 2TT for which tan e V3 3

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Q: Detemine the value OF C IF X=1-co2 and y =1.B9 when you evaeuate Scot"(2x)dx. Cure radiar form Of…

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Q: Ise radians. sin (5h) lim h>0

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Q: The value of Sinh(3i) is A)-i sinh 3 B)i sinh 3 C)i sin 3 D)-i sin 3 E)none

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Q: For which value of a is the length of the cardioid r = a(1+ sin 0), 0 < 0 < 2ñ _32 units? 6 2 -4 -2

A: Solution

Q: Find the value of all six trigonometric functions for e = 4 %3!

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Q: 5. What is the sine ratio of zZ? 16 12 20

A: Given ,

Q: 15. Evaluate Sin x cosx dx 2x Your answer 16. Evaluate se 3cos 2x Sin 2x dx Your answer

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Q: 47. A direct calculation shows that 2 sin? x dx = . How close do you come to this value by using the…

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Q: ompala. 2. Detemine £{e3t sin 6t – t3 + e'} using table comparison method.

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Q: A ball on a spring is pulled 4 inches below its rest position and then released. After t seconds,…

A: Given: The ball's distance, d in inches from its rest position is d=-4 cos π3t. Find t for d=-2.

Q: a)Salve sin 2x-cosx-0 algebraicaly for kne damds - TEx<T. 6) Sdlve csc'x= 4 cot'x algebraically.…

A: sin2x-cosx=0⇒2sinxcosx-cosx=0 [Since, sin2x=2sinxcosx]⇒cosx(2sinx-1)=0⇒cosx=0  or…

Q: 3) Solve the following for the angle 0 using CAST Rule, where 0 ≤ 0 ≤ 360 a) sine === b) cost = -√3…

A: Given that, a) sin θ = -12 b) cos θ = -32 By using CAST rule, find the angle θ. CAST Rule: If the…

Q: b. sin? () = 2 over [0, 2n) %3D

A: EXPLANATION

Q: 2. Using trigonometric substitution, what is S x² -9 dx ? x3

A: Given integral √x^2-9 /x^3 dx

Q: V14 Let 0 be a quadrant Il angle with sin(0) || 5 Find cos

A: The trigonometric identities can be used here, sin2(θ)+cos2(θ)=1 cos2(θ)=2cos2θ2-1

Q: du is? x³ sin (x?) dx is evaluated using IBP, the value of v du When A sin (x2) 2 B none of the…

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Q: tind the geneval solurion to the D.E 4) (3) you Know that 4o)s sinx is one of the solurions

A: We will find out the required general solution for given differential equation.

Q: V2 cosy = 7, and angle x and angle y are both in the first quadrant. sina = %3D tan(x+y)=

A: We can find the answer as below.

Q: 3) Solve the following for the angle 0 using CAST Rule, where 0 ≤ 0 ≤ 360 a) sine === √√3 b) cose =…

A: a) sinθ=-12 By CAST rule, sinθ is negative in 3rd and 4th quadrant, So here 180≤θ≤360. Since period…

Q: 2. Evaluate the following using trigonometric substitution. Show all necessary solutions. 2/2 dx (c)…

A: We are given the integral : ∫12dxx24-x2 We need to evaluate this using trigonometric sub:stitution .…

Q: A ball on a spring is pulled 6 inches below its rest position and then released. After t seconds,…

A: we have been given that a ball on a spring is pulled 6 inches below  its rest position and then…

Q: 4. Write an equivalent expression for sin*(x) that does not contain powers of trigonometric…

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Q: (c) Using the hyperbolic identity cosh² r – sinh r = 1, and without using a calculator, find all…

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Q: 2. sin 8 = 42 P(0) is in the second quadrant

A: Given θ lies in the second quadrant We know that sinθ , cosecθ are positive in the second quadrant…

Q: x +a -)| < 2lsin(",") х — а If 0< lar – al < 8, then Isina-sinal = |2cos(",")sin(,")| х— а |2cos ("

A: Given: 0&lt;x-a&lt;δTo prove:sinx-sina=2cosx+a2sinx-a2≤2sinx-a2