For each expression that follows, replace x with 30  0, y with 45  0, and z with 60  0, and thensimplify as much as possible.     6 cos x

Q: Evaluate the following expression. sin?() + cos²(}) O1/4 O1/2 1

A: Given that: sin2π6+cos2π3

Q: Evaluate each of the following if x is p/2 and y is p/6.          cos (x-y)

A: cosx-y

Q: Find the exact value of sin -) given csc(x) = 8, for 90° < x< 180°. 3/7 + 16 1 37 А. + С. 2. 2 1 37…

A: Given; Csc(x)=8 90°&lt;x&lt;180° Repost the next image question.

Q: Simplify the expression V125 - 5x2 as much as possible after substituting 5 sin(e) for x. (Assume 0°…

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Q: Find the exact value of the given expression. con(2 tam (4) cos 2 tan

A: 1

Q: For the expression that follows, replace x with 45° and then simplify as much as possible. 8 cos(2x…

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Q: Evaluate each of the following expressions when x is p/6. In each case, use exact values.     sin 2x

A: The given expression is sin2x

Q: Given the following: sin a = and < a <n and cos B = - and n *<p<플 %3D |

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Q: For the following expression, find the value of y that corresponds to each value of x, then write…

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Q: O Find Hhe lme qr=sin'o when the elpe 3.)

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Q: Evaluate each of the following if x is p/2 and y is p/6.        cos (y- pi/6)

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Q: Evaluate the following : e#/2 (a) sin(In 0) dê.

A: SOLUTION-

Q: For each expression that follows, replace x with 30  0, y with 45  0, and z with 60  0, and…

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Q: 2 cos 0 Só 3 rsine drdð 3

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Q: For all values of 0 for which the expression is defined, =? tan20 Select the correct answer below: O…

A: The given expression is cos2θtan2θ. Formulae Used: cos2θ=1-2sin2θtan2θ=cos2θsin2θcot2θ=1tan2θ

Q: For each expression that follows, replace x with 30  0, y with 45  0, and z with 60  0, and…

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Q: 3. Given AMNO, which represents the value of cos(O)? * 40 50°

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Q: 7. S sin? x dx

A: The given question has been solved in detail

Q: Rewrite the following expression in terms of the given functions. 1 cos x and sin x tan X+ cot x

A: We have to Express

Q: Which of the following is equivalent to 4 sin? x cos? x- 1? O - sin 2x | O cos? 2x O- cos? 2x | O…

A: Which of the following is equivalent to  4sin2x cos2 -1 ?

Q: Given the following: sin a = and < a <n and cos ß = - and n< <B < a

A: Given: sinα=13, cosβ=-13; π2&lt;α&lt;π, π&lt;β&lt;3π2 we know that cosA+B=cosAcosB-sinAsinB…

Q: If 180° < 0 < 270° and cos : -, find cos 7 15 O V15 15 O 2v15 15 2/15 - 15

A: Given:- cos θ = -715 and   180°&lt;θ&lt;270°  To find  cos θ2.

Q: For each expression that follows, replace x with 30  0, y with 45  0, and z with 60  0, and…

A: Given, 2 cos ( 900  -z) and z=600

Q: Evaluate the following given sint cos? x dx. (Identify u and du)

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Q: For the following expression, find the value of y that corresponds to each value of x, th 37 y = 2 +…

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Q: Make the substitution u = 7 cos e in the expression 1/V 49 - u2, and simplify the result. (Assume…

A: Make the substitution u=7cosθ in the expression 149-u2.

Q: For each expression that follows, replace x with 30  0, y with 45  0, and z with 60  0, and…

A: We have to simplify: -3 sin 2x where,  x=30°y=45°z=60° So putting x=30° in the given expression: -3…

Q: . If 180° <0 < 270° and cos 0 = -, find cos . 15 O 2v15 15 O - VI5 15 O V15 15 O - 2V15 15

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Q: Write the given expression as an algebraic expression in x. cos( cos 4») COS X)T SO

A: Recall:  cos (2x)=2cos2(x)-1 Given,  cos12 cos-1x

Q: For the expression that follows, replace x with 30° and then simplify as much as possible. 8 cos(3x…

A: Given expression is,

Q: Evaluate each of the following expressions when x is p/6. In each case, use exact values.      cos…

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Q: For θ between 0° and 360°, find the two values of θ that satisfy the following.  cos θ = √2/2

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Q: For each expression that follows, replace x with 30  0, y with 45  0, and z with 60  0, and…

A: Definition used -  Value of trigonometric ratios-                          sin (30°)=…

Q: Evaluate each of the following expressions when x is p/6. In each case, use exact values.     1/2…

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Q: Given cos*(4x) - sin*(4x) = cos(g(x)), determine the value of g(x). А. 4х В. 8х С. 16х D. 32x

A: We have to determine the value of the polynomial gx which satisfies the equation…

Q: Ind a and b entiable everywhere. S7 cos(x) if x < 0 f(x) = %3D ax + b if x 20 a = b = Need Help?…

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Q: Given cos*(4x) - sin*(4x) = cos(g(x), determine the value of g(x). А. 4х С. 16х В. 8х D. 32x

A: To find the value of g(x) use the following formulas. sin 2x + cos 2x = 1 x2 - y2 = (x - y)(x + y)…

Q: Evaluate the followingintegrals.

A: It is given that, ∫0π4cos28θdθWe have to evaluate it.

Q: Find the value of the following tanh(  1 – j )   Answer must be.  1.084 – 0.2717i

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Q: For each expression that follows, replace x with 30  0, y with 45  0, and z with 60  0, and…

A: Given:           2 cos(3x - 450) To replace x with 300, y with 450 and z with 600

Q: Which of the following expressions is equal to the given expression below? 1-c O s 8x 1+c oS 4x V1 –…

A: 1-cos8x1+cos4x

Q: Evaluate each of the following if x is p/2 and y is p/6.        sin ( x + pi/2)

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Q: d sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form. 12 15 D=| E = |…

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Q: Which of the following expressions is equivalent to -? Cos a cos a 1-cos a a. c. 1- sin? 1+cos a d.…

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Q: Evaluate the following expression when x is 1/6. Use exact values. 6 co(2x + 5) 3

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Q: Find the value of x. Round to the nearest tenth. Sin = opp cos = adi tan = opp hyp hyp adj 3 4 10 28…

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Q: Find the exact value of cos e 13 15 O 15 17 28 O 2 17 15 13

A: Cos = base/hypotenuse

Q: Evaluate the following expression when x is t/6. Use exact values. -- sin(3x – 7) 2 8 3

A: The exact value is :-

Q: What is the approximate value of 0, if cos 0 = 15? O A. 58° ОВ. О В. 32° Oc 28° O D. 62° O E. 48°

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Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.