4.6 Trigonometric Identities 1. Consider the equation cos x tan x =1. sin x a) Show that it is true for x = 30°. b) Show that it is true for x = 45°. c) Show that it is true for x = %3D 60°.

Q: Find the exact values of the remaining trigonometric functions of satisfying the given conditions.…

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Q: 4 5. Given that sin 0 and tan 0 < 0. Find the other five trigonometric functions of 0 5

A: Given that sin(θ)=-45 and tan(θ)&lt;0.We have to find other five trigonometric functions of θ:

Q: 9. Given that sin A= 5 , where OCA<II, and tan B = -4, and tan B= 4 2. %3D 3. where 3 TT <B <2 Tl,…

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Q: 7. Given that tan (A) = - and angle A is in 3rd quadrant and cos(B) = - and 13 angle B is in 2th…

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Q: 7. Let tan u = and sin v = , with n <u < and < v<T. Find the exact value of sin(u – v). 13

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Q: 15 Find the exact value of the trigonometric expression given that sin(u) = -, where 3T/2 < u < 27,…

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Q: 8. If cos(a) = -, and tan(a) is positive, find the other five trigonometric functions for a. Find…

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Q: 6. Explain the steps in verifying that the following equation is an identity. sec x sin x = cot x…

A: We have given equation  Taking left side of equation  LHS = secxsinx-sinxcosx           =…

Q: 4. Explain the steps in verifying that the following equation is an identity. sec sin a sin r cos a…

A: Given equation: secxsinx-sinxcosx=cotx

Q: 4. Express the following as a single trigonometric ratio: a) 4sin(2x)cos(2x) b) 6cos? 3

A: We have to express the given trigonometric ratio in a single trigonometric ratio.

Q: 3 5 3n If cos x = - 5 , where sin (x - y). , and cot y = 12 , where 2 determine the exact value of

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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: Find sin(2x), cos(2x), and tan(2x) from the given information. cot(x) = x in Quadrant I

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Q: 2. (20 pts.) Let cos() =- and <B< Use one of the Half-Angle identities to find the exact value of…

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

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Q: a. Let cosx = (-) and cos x lies below the x axis. 2+0 Find sin(2x), cos(2x) and tan(2x). b. Proof…

A: In case of first question we find the solution of X. Then find the other expression.

Q: According to Snell's law, the angle of refraction θ2 of a light ray traveling in a medium of index…

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Q: 7. Given 0, a positive angle less than 2n, fill out each of the following in terms of 0. e in QI e…

A: Trigonometric identities used:  1. sin(-θ) = -sin(θ) 2. cos(-θ) =cos(θ) 3. sin-1(-θ) = -sin-1(θ) 4.…

Q: 7. Find the exact value of tan 6 + sin 0 for the angle 0 shown. 3

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Q: 3 Given that the cos(0)= and is in the first quadrant, what is the exact value of sin(20) ?

A: Given that: cos(θ)=35  and θ is in first qudrantWe know that sin2θ+cos2θ=1substituting  cos(θ)=35…

Q: 2 then which of the 5 An angle e drawn in standard position terminates in the fourth quadrant. If…

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Q: 3 7, x in quadrant I, then find (without finding x) : 4 If sin z sin(2x) cos(2r) tan(2a)

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Q: 2.) Use the given information to find the exact value of tan( ). , 0 < a < 5 11 sin(2 61 » 2

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Q: 6. Given tanx =where x is an acute angle, and tan y =-2.4 where y is an obtuse angle. Without the…

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Q: 11. Given that 0 is an acute angle and sin 0 trigonometric functions of 0. find the exact values of…

A: θ is acute so it's in first quadrant. All the trigonometric ratios will be positive.

Q: 8. Find the exact value of the indicated trigonometric function of 0. /5 cos e tane 3' 2 Find sin 0.

A: The value of trigonometric ratios is, cosθ=23 tanθ=-522

Q: 2. If tan 0 =, 0 E Q II, find the other five trigonometric functions. %3D

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Q: Indicate the quadrant e where e belongs to satisfy the following conditions: + sin/csc all + +…

A: To identify the quadrant where the angle θ belongs.

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: 1 Suppose that cota= and - <a<T. <a<n. 2 Find the exact values of sin- and tan- 2 2 JT

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Q: Find the exact value of the trigonometric expression given that  sin(u) = −  3 5,  where  3?/2 < u…

A: sin u= 1-cos2u sin(u + v) = sin u cos v +cos u sin v

Q: B/ Find sec a, sin a, csc a, tan a and cot a, if a =. -1 V3 = COS 2

A: Given query is to find indicated trigonometric functions.

Q: 9 Find the exact value of cos e and cot0 given csc 0 =2 and tan e<0. Show all work. 7

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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: 8 sin(x) x in Quadrant I 17

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Q: 1. Determine an exact value for the following expression: sin COS IL + tan It cot 3 4 4

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Q: 1. Given that sin(a) = with 0 < a < 5, give an exact answer for the following: a. sin() b. cos() %3D…

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Q: 24 Given that sin(0) =- and 0 is in Quadrant III, what is cos(20)? %3D 25

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Q: 15. Explain the steps in verifying that the following equation is an identity. sec a sin e sin a cot…

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Q: (1) Use the trigonometric identities for sin A sin B, sin A cos B, and cos A cos B to show that |…

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Q: Find the exact value under the given conditions. 4 TI 18) sin a =<a<n; cos ß =, 0<B< 0 < B<2 Find…

A: Given: So, alpha is in the second quadrant. There cos is negative

Q: Find the exact value of the trigonometric expression given that  sin(u) = −  3 5,  where  3π/2 < u…

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Q: ) 1- Given that a = sin Find cos x, tan x, cot x, secx and csc x ?

A: This is a problem related to the trigonometric ratio. We will find out value of alpha in degree and…

Q: 5. Determine the value of sin(arctan(3)+arctan(2)) using the trig identity sin(A+B) = sin(A) cos(B)+…

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Q: 8. Given that sin 0 = , and the angle 0 is in the first quadrant, find the value for cos 0.

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Q: 7) Given that tan(a) = with a in QIII and cot(B) = --with B in QIV, find sin(a +B) and cos(2a). %3D…

A: Given : tan(α)=23 with α in QIII and cot(β)=-14 with β in QIV. The objective is to find the value of…

Q: Question in Image.

A: At the outset I must say it's an amazing question. Information is given about α and the questions…

Q: 2. Given that sec a = - 9 and <asn find exact values of the requested trig functions. sin a tan a…

A: Given:secα=-9sinα=1-cos2αtanα=sinαcosαcscα=1sinα

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.