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 b Hence find, correct to the nearest minute, the acute angle x that satisfies the equation 2 cos x - sin x = 1.

Q: Verify the identity. 4 cos(sin-1 x) = V 16 – 16x? Let e = sin-1 x = sin e = x = X. * Thus, 4…

A: Explanation of the answer is as follows

Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: (2) If 5 Sin A +3=D0 where A E]T, [, and 25 Cos B -7=0 where BE] 2n [, then find the value of Sin…

A:

Q: Find the exact value of sin(20) given sec e 11 and 0<e <". 2-4-V112-4 А. 3-3-V13-92 С. 112 132…

A:

Q: 2 Given tan 0 = -and sin 0 > 0, find cos 0. %3D Cos 0 _ 3/13 13 О А. O B. cos O 0 = 3/13 COS %3D 13…

A: The given data is: tan θ= -23  and  sin θ&gt; 0

Q: 3. Suppose that sin r =, x lies in quadrant I, and sin y = 3 and y lies in quadrant II, find sin(x +…

A: Given: sinx=45, x lies in quadrant I. And siny=1213,y lies in quadrant II. We know that, In quadrant…

Q: cos(1) dt Using an appropriate substitution, evaluate: [2 + sin(1) ]* ™ 3 A +C [2+ sin(1) ]} B 3[2+…

A:

Q: 2. If tan 0= x2, which of the following is correct? Defend your answer. a. cos 0 = 1/V(1+x^4) b. sin…

A: The solution for the above question is as shown below

Q: Express the number 2/3 – 3i in the form R(cos(0) +i sin(0)) = Re", where R> 0 and -7 < 0 <T. NOTE:…

A:

Q: From the formula for cos (t + t) find cos (2t) in terms of sin t.

A:

Q: B) 1- Given that a sin %3D Find cos x,tan x, cot x, sec x and csc x ?

A:

Q: 2. If tan 0= x2, which of the following is correct? Defend your answer. a. cos e = 1/V(1+x^4) b. sin…

A: As per the guidelines I can solve only one question

Q: 3 Given sin 0 = - in TT 0 < 0 < =, find the five remaining trig functions. 2

A: We find the remaining trigonometry function

Q: Using an appropriate substitution, f sin³ (x)cos®(x)dx is equal to: sinx + C sin13x + C 13 sin11x…

A:

Q: 9. The position of a moving particle as a function of time is given by: x = (4 - 0.11) sin(0.81)…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Express the number 5/3 – 5i in the form R(cos(0)+ i sin(0)) = Rei where R> 0 and -T <0 <T. NOTE:…

A: Given:     A complex number z:=53-5i. To Find:  The Polar form of z. i.e., z=Reiθ=Rcosθ+isinθ, where…

Q: Which of the following is correct in solving 3/22 2x√2 + x dx? Trigonometric substitution can be…

A: To determine which of the following is correct in solving ∫2x2+x dx.1 Trigonometric substitution can…

Q: Express the number 7/3 – 7i in the form R(cos(0) + i sin(0)) = Re", where R>0 and -n < 0 < T. NOTE:…

A: Given complex number is 73-7i Let 73-7i=Rcosθ+isinθ                       . . . (1) where R&gt;0 and…

Q: Given 0 2 O 0, T

A: Use the tangent ratio to simplify the equation and then solve for .

Q: Find the exact values of sin and cos for sin e= on the interval 0° s es 90°. 2 sin 0.1691, cos…

A: We know that,  cosθ=1-sin2θ         cosθ&gt;0 in 0°≤θ≤90°        ⋯⋯1sinθ2=1-cosθ2…

Q: 3. Find all angles 0 between 0° and 180° satisfying the given equation. V3 A. sin 0 = 2 B. cos 0 = 2…

A:

Q: S By an appropriate trigonometric substitution, S: I 1 √10 sin 0 cos² Ode Cos 0 10 sin 0 -do |…

A: Here we will use Trignometric sunstitution for given integral.

Q: Q5. a) Suppose tan x = - and x is in the second quadrant. Then find: (i) sec x (ii) cos x (iii) sin…

A:

Q: Express the number 2/3 – 8i in the form R(cos(0)+ i sin(0)) = Reo, where R> 0 and -T <0 <T. NOTE:…

A:

Q: Approximate to four decimal places, when appropriate.

A: To evaluate,

Q: 12. Given that V3 cos x = cos(-x), tan x= A 3. cos(f B V3 C 1. V3

A:

Q: Find all solutions to the equation 3 sin r – 4 = sin r – 2 in the interval [0, 27].

A: Given 3sinx-4=sin x-2

Q: How many values of 0 in the interval 0 < 0 < 2T satisfy 1 – 3 sin 0 + 5 cos 30 = 0? %3D (A) 2 (B) 4…

A: The aim is to determine the number of values of θ in the interval 0≤θ≤2π satisfies 1-3sinθ+5cos3θ=0.…

Q: Find tan 5, given that tan x = 3 and t<x< 2 10 +1 O A. 10-1 OB. V10 - 1 Oc. V10 + 1 OD. 3. 3. 3.

A:

Q: Eliminate the parameter t from the following. x = sin t − 3, y = cos t − 2

A: Eliminate t by squarring

Q: 1) Using the formula: cos(x + y) = cos x cos y - sin x sin y, prove in steps that: cos? x = 1+cos 2…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find sin(t) and cos(t) for the values of t whose terminal points are shown on the unit circle in the…

A:

Q: 3. Given 0 < 0 < 27, solve 2 tan 0 + sin 0 cos 0 = 0. 2 0, T

A: Given:    2tanθ+sinθcosθ=0           ,           0≤ θ&lt;2π

Q: Suppose that sin(a) = 4/5 and cos(b) =4/7 define in the first quadrant, determine tan(a+b). (round…

A: Given, sin(a) = 4/5 ------equation 1 cos(b) =4/7 ------equation 2

Q: 7) Use the given figure to write the trigonometric ratio as fractions and as decimals rounded to the…

A:

Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

A:

Q: Find the exact value of sin​(u​-v) given that sin u= 5/13 and sin v= 8/17​, with u and v in quadrant…

A: In the question we have to find sin(u-v).Where u and v are in first quadrant.

Q: 2. If x = 2 sec 0 and 0<0< T/2, then %3D (a) sin 0 = (b) cos 0 (c) tan 0 =

A:

Q: 1. Determine solutions to sin 2x , xE [0, 2x) 2x = sin () 2x 0.73 %3D accurate to 2 decimal places.…

A:

Q: one of sin x, cos x, and tan x is given. Find the othertwo if x lies in the specified interval.

A: Given information: tanx=12    x∈π, 3π2

Q: If sin a cos 31° + cos z sin 31° =0.7, then the value of x, where 0° <x <90°, to the nearest whole…

A:

Q: and <B<m 6. Given sin B = %3D 3' 2 Give the exact values for cos B and tan 3 V5 tan 3 3. 2/5 cos B =…

A:

Q: 2. If sin a =,0<a< 3. 2V5 ,where <B < 2n 3 . cos ß = Determine the value of a. sin(a + B)%3D b.…

A:

Q: Solve the equa tion on the interval [ o, 2 ) 2 sin? 9-3 sin O +1 =0 tan2x-1 =0 (2 cos x +JE) (2 sin…

A: As per bartleby guidelines we only give first three question answers.

Q: let's consider the equation y' + (cos x) y = e -sin x i) Show that any solution (which we will call…

A: Let us consider a differential equation of the form  Then the solution  of the differential…

Q: 3. (a) Use the substitution x = 2 tan 0(-1/2 <0 < T/2) in the expression T/V4+x2 and show the result…

A:

Q: Express the number 8/3 – 6i in the form R(cos(0) + i sin(0)) = Re", where R 0 and -T <0 < T. NOTE:…

A: Please check step 2 for solution

Q: Compute the indicated sin α = 15 17 cos B = cos = (a) (b) - 4 5 quantity using the following data.…

A:

Q: 9. Find all values of x in the interval [0,360°) that satisfy each equation. Round approximate…

A: a) 2sinx=cosxsinxcosx=12tanx=12x=tan-112x=26.6°, 180°+26.6°x=26.6°, 206.6°