Find the quadrant in which the terminal point determined by t lies if            a. sin(t) < 0 and cos(t) > 0              b. sin(t) > 0 and cos(t) > 0

Q: Find the EXACT expressions for the indicated quantities, given that: cOS 는 /2+v3 sin 를 COs and

A: Here, first we will find will find the values of sin(π/12) and then,to find the value of tan(π/12),…

Q: Find sin(s - t) given that sin s= -5 with s in quadrant IV, and sin t= with t in quadrant II.

A: Given data:     The first given value is: sin s = -1/2. The second given value is: sin t=1/4.   The…

Q: 3 x in quadrant I, then find (without finding x) : If sin z 5 sin(2x) cos(2x) = tan(2x) = ||

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Q: If cos t = - and t is in the 3rd quadrant, then sin t = V48 4 V80 8 V48 8 O V48 4

A: Since, it is given that cos (t)=-48and t is in the 3rd quadrant.Our Aim is to find sin (t)=?

Q: the terminal point P(x,y) determined by a real number t is given. find sin(t), cos(t), and tan(t).…

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Q: Reduce sin θ + 2 cos θ to the form r sin(θ + ϕ), and find ϕ

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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: 4. State the quadrant in which 0 lies. a) cos 0 > 0, tan 0 0

A: Introduction: All sin tan cos rule: All sin tan cos rule is all trigonometrical ratios in the first…

Q: The value of (cos*x sin xdx а. 0

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Q: 3 x in quadrant I, then find (without finding x) 4 If sin x - sin(2x) I %3D cos(2x) tan(2x) : %3D

A: use trigonometric ratio to find the trigonometric function

Q: 2. Write sin(t) in terms of cos(t) for t when t lives in quadrant III

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Q: Find A°, where (cos(7/5) -sin(T/5)) A = sin(T/5) cos(T/5)

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Q: Find the exact value. a. sin-1(sin 0.8) b. sin(sin-1 1.3) cos(cos-1 n) с. d. cos(cos-1 –0.4)

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Q: COs 0 , where r<0< 4 tan 8 =, where 0 <B< What is the exact yalue of sin (A i An

A: Given,            cosθ=-34, where π≤θ≤3π2            tanβ=34, where 0≤β≤π2To find : What is the…

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

A: We will use a unit circle. Unit circle is of the form cosθ,sinθ

Q: Find the exact value of cos 2a given that sin a = x=% and 1 180° < a < 270°.

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Q: Determine the exact value of sin(x y) given the information below: <x < TT, <y< 2T, cosx = - -<y<2T,…

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Q: =-5 13 sin(x) : x in Quadrant II

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Q: Find the value for x, where 0≤ x ≤ 2ñ 4 sin x + cos2x =2

A: For a quadratic equation of the form: ax2+bx+c=0, the roots are calculated using the formula: x1,…

Q: Given sin(a) = and 0 < a <T/2, find the exact value of sin(a/2).

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

A: Given, t is terminal points on the unit circle shown in the figure. t increases in increment π6

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

A: Simplification

Q: (a) sin(e/2) (b) cos(e/2) (c) tan(8/2)

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Q: Assume that a particle’s position on the x-axis is given byx = 3 cos t + 4 sin t,where x is measured…

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Q: 4. Find the value of cos (A+B) for A terminating in quadrant III and B terminating in quadrant IV…

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Q: 1) Use Excel to plot both of sin(x), cos(x) at the same plot, where: 0<x <2n.

A: To find- Use Excel to plot both of sinx, cosx at the same plot, where: 0 ≤ x ≤ 2π.

Q: Find the exact value of the trigonometric expression given that sin(u) = - where 37/2 <u< 2x, and…

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Q: Given sin a =with 0<a< 90°, find cos 2a and tan a/2.

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Q: When t = 0, AP = ..... so sin t will begin at a value of 0. As t increases from 0 to 7T/2, sin…

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Q: Use the unit circle to find all values of 0 between 0 and 2n for which 1 sin 0 V2

A: For the solution follow the next step.

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

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Q: 3) Find sin(s+ t) given that cos s = with s in quadrant I, and sin t = - with t in quadrant IV. 2

A: We are solving the first question and for the next question post the question again and also mention…

Q: Use the given information to find (a) sin(s + t) . (b) tan (s + t) , and (c) the quadrant of s + t .…

A: We use Pythagoras theorem and Trigonometry ratios

Q: Given sin(a) = and 0 < a < T/2, find the exact value of sin(a/2).

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Q: l side of θ lies along the lin

A: we have to find sin θ and cos θ if the terminal side of θ lies along the line y = 4x in QI

Q: What is the frequency of the periodic function f(x) = 5 sin()?

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Q: express the given quantity in terms of sin x andcos x. sin (2π - x)

A: expression in cosine and sine form of sin2π-x We used identity:  sinA-B=sinA cosB-cosAsinB

Q: 2. Given sin a = with 0< a < 90°, find cos 2a and tan a/2.

A: Using trigonometric formulas

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

A: Concept : Circle whose radius is r and centre at origin ; coordinate of any point on that circle…

Q: The value of (cos x sin xdx =

A: It is definite integration problem.

Q: Suppose v is in the interval G,n), with tan v =-11 Find the exact expression for the indicated…

A: tan v=-11v=tan-1(-11)v=95.2°

Q: Given that the value of sin x – cos x = -1/3, find the numerical value of sin 2x.

A: We have to find

Q: From the formula for sin (2t + t) find sin 3t in terms of sin t.

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Q: A rain gutter is to be constructed from a metal sheet of width 54 cm by bending up one-third of the…

A: Area of part 1,Area of triangle = 12×b×hb= 18×cosθh= 18×sinθArea of triangle 1 =…

Q: If cos t =- and t is in the 3nd quadrant, then sin t

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Q: Find the exact value for the expression under the given conditions. 5 5 cos (a +ß), sin a = - for a…

A: Out of the six trigonometric ratios , two ratios are positive in 3rd quadrant i.e.tanx and cotx and…

Q: 15 Find the exact value of the trigonometric expression given that sin(u) = - where 31/2 < u < 2n,…

A: we have given sin u =-35  (IVth quadrant) ⇒u=sin-1(-35) =-36.87° or 323.13°cos v =1517 (Ist…

Q: 2 x in quadrant I, then find (without finding x) If sin x = sin(2x) cos(2x) tan(2x)

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Q: 14. Find sin 0, given that cos0=Y,and tan 0 <0. V5 V59 a.- 8 5 C.- 8 d

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.