7. Find the maximum and minimum values of the expression 2 cos 0-4sin 0. Hence, determine the angles at which they occur if 0° <0<360°.

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A: First of all use the trigonometric identity that is cosα=1-2sin2α2 and now substitute -35 in place…

Q: 4. Apply half-angle formula to find a. cos 15° b. sin 15° C. COS

A: Given: cos15∘, sin15∘, cos5π8 We know that cos2x=cos2x-sin2x…

Q: (4) Find all the angles frem o to 360° which satisfy the equation COS X %3D

A: We have to find out the angle

Q: If a, B, y, ð are the smallest positive angles in ascending order of magnitude which have their…

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Q: 15 Suppose that tan ɑ = and 90° <a < 180°. 8 Find the exact values of cos 5 and tan-

A: Given, tanα =-158, 90°&lt;α&lt;180°

Q: 3 If tan 0 2' T < 0 < find the exact value of each of the following. 2 (c) sin 2

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Q: 19 If x= cos 30 and y = sin 30 , then O a.-3 cot 30 O b. 3 tan 30 O C.-3 tan 30 o d.- cot 30

A: We have to find the differentiation like in the parametric form of differentiation . We have the…

Q: between 0° and 360°. z, = cos 100° + i sin 100° Z2 = cos 230° + i sin 230° %3D Choose the correct…

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Q: 15 Suppose that cos 0 = and <0<n. 17 2 Find the exact values of sin- and tan 2

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Q: 3 12 6. Gtven sina = -; and cosß = where n<a <: and <B< 2n. 5 13 Draw the triangles, length of the…

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Q: 7. Find the maximum and minimum values of the expression 2cos 0-4 sin0. Hence, determine the angles…

A: Given function can be written as…

Q: 4 5. Find the exact value of sin 105° using half-angle identity. 2+ V3 А. V2+ v2 С. B. V2 + V3 D. V2…

A: Given:  sin105o

Q: If 0 be a positive acute angle satisfying cos² 0 + cos“ 0 = 1 then the value of tan² 0 + tan“ 0 is

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Q: B. Solve for the acute angle of angle 0 for each that satisfies the given condition. 1. sec 30 = cSc…

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Q: -57 If 0 -, then 6. sin(0) = %3D cos(0) = %3D

A: θ=-5π6 find the value of  sin(θ) sinθ=sin-5π6 sinθ=-sin5π6 sinθ=12

Q: Assume that 0 ≤ θ &lt; π/2.

A: Given that

Q: 15 Given: sin0 and %3D 17 2 Find the exact value of: cos 2 cos

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Q: 15. Use Double- or Half-Angle Formulas to solve in the interval [0, 2n). 2 sin? 0 = 2 + cos 20

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Q: 13 Suppose that sec and 270° <0 < 360°. 0 Ө Find the exact values of sin and tan 2 2 गंत

A: Solution of given question is written in below steps.

Q: 22. Given that4 cos 0 + 3 sin 0 = R sin(0 + a), the value of R and tan a are respectively 3 A 25…

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Q: 8 17 3 3. (Trigonometry) If sin(a) 음 where 0 < a < 5 and cos(B) 2 where 5 IT * < B < 2n, find the…

A: for simplicity use  here we have

Q: 2. Find the exact value of the following expressions: а) sec-- cos + sin b) sin 12 4 6

A: topic - trigonometric ratios

Q: 5. If sin e and 360 < e< 450°, find cos %3D

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Q: 2. Find the exact value of the following a. cos 12 b. sin (70°) cos (40°) – cos (70°) sin (40°)

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Q: 5. 3 If tan B = - with * <B < 2n , find cos (2ß). %3D

A: It is known that in the first quadrant all trigonometric ratios are positive, in the second quadrant…

Q: 5. Without a calculator, find all the exact values of 3 cos(46) – 2 sin(86) sin(46) = 0 17T <B< 0.…

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Q: 2.12. Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas given that…

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Q: (b) If cos (20) = 3/5 and 0 <0 ST/4, find the values of i. sin (20) %3D ii. cos (0) iii. sin (0)

A: If the angle belongs to  0≤θ≤π4, then 2θ belongs to0≤2θ≤π2          It means 2θ is in quadrant I…

Q: and 9o c oc 180 Sin e = Gf Cos 2 SUPPOSE that find exact values and tan 2. Cos tan

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Q: (a) The solutions of the trigonometric equation tan(30) +1 = 0 are: 37 kT ; + ka (i) + kT (ii) 4…

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Q: 37 Determine cos(2.4) given that tan A =-, where A<A<- 2. 1/3

A: Given: tan A=13 to find cos2A where π≤A≤3π2 The formula for cos2A=2cos2A-1 or cos2A=1-2sin2A or…

Q: 5 1. If sec a with a in quadrant Il and cos B = with B in quadrant IV evaluate: 3 a) sin(a- B) b)…

A: If sec α=-52 with α in quadrant II and cos β=13 with β in quadrant IV, then to evaluate the…

Q: Suppose cos(α)=−3/4 and sin(α) is negative. If the point (−3,y) is on the terminal side of the…

A: Use trigonometric ratio  &amp; its identity

Q: 4 3. Given cos 0 determine tan 20 - -

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Q: (금) 7 Suppose that is an angle in quadrant 3 and that cos y = Compute the exact value of sin 25 sin…

A: Given, cosγ = -725  γ2 is an angle in quadrant 3  We have to find the exact value of sinγ2.

Q: 17 Given that cos 0= <0<T, find the exact value of each of the following. 3 2 (a) sin (20) (b) cos…

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Q: 4 The value of [ cos* 30 sin° 60 de is

A: We need to calculate the given definite integral for which we will use the substitution.

Q: 8. 15 Use the figure above to find the exact value of sin 20, cos 20, tan 20. sin 20= cos 20= tan…

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Q: 2. If cos 4A = 23/49, find tan A %3D

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Q: 12 Determine the exact value of sin 20 given that cos=- and 13 3π 2 π<0< without determining the…

A: Concept: Trigonometric ratios: sinθ=PH; cosθ=BH Where P is perpendicular , H is hypotenuse and B is…

Q: 1 Assume that cos(0) and 0 is in the first quadrant. Compute the following using the double 5 angle…

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Q: 2 /5 If cos(a) = - with π<α< compute the exact value of the following: 2 cos(2a)=| sin 2 tan 2

A: To find the required values we need to use the double angle formula and the half angle formulas.…

Q: Determine the exact value of cos(330)° V3 2

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Q: 2. Find all possible solutions to the equation 2 cos 0 + v2 = 0. 0 in radians and let k represent…

A: To Determine: find all possible solutions to the equation .Express θ in radians and let k represent…

Q: Find all values of 0, 0° < 0 < 360°, that satisfy 5 cos 20 + 7 sin 0+1 = 0

A: 5cos2x+7sinx+1=0REwriting we get:6-10sin2x+7sinx=0sinx=-12, sinx=65Combine all the…

Q: 5 If sin u = 13 12 cosu = 13 3 and cos W = 5 W = --, find the exact value of each of the following:…

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Q: 2. Find all possible solutions to the equation 2 cos 0 + v2 = 0. O in radians and let k represent…

A: The given trignometric equation is2cosθ+2 =0

Q: 1. Find the values of sin 20, cos 20 and tan 20, given: 9 3n a. tan 0 if n<0 < 40 2 3n b. sin 0 if <…

A: Giventanθ=940 ifπ&lt;θ&lt;3π2sinθ=-12 if 3π2&lt;θ&lt;2π.To findsin2θ, cos2 and tanθ

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.