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.     5 sin 2 y

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

A: Given that: sin2π6+cos2π3

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: Which of the following is not in the domain of cot(x)? Select all correct answers. Select all that…

A: We need to select those options which are not in the domain of cot x. We must know that domain of a…

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

A:

Q: Write the following sin(2arccos(3x)) as an algebraic expression in x 1/3. for -1/3 less than or…

A:

Q: Evaluate the following and show all necessary solutions. Enclose your final answer. tan? x (1+ sin?…

A: The given integrals are; 7. ∫tan2x1+sin2xcos2xdx8.∫-134x-5dx

Q: Find the numerical value of each expression. (a) sech(0) (b) cosh-(1)

A:

Q: y = cot2 ( sin(0)).

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

Q: sin x xp = + cos x 1+c

A: ∫0π2sin x1+cos xdx Formula ∫xndx=xn+1n+1+C

Q: Solve the following: 12 sin? x – z = 0 Z=5

A: Solve the equation:              12sin2x-5=0

Q: Evaluate the following expression when x is t/6. Use exact values. sin 2x

A: Given query is the find indicated values.

Q: For all n and m, evaluate: " sin na cos ma da

A: We have to solve given integration  ∫-ππsin nx·cos mx dx

Q: Evaluate each of the following expressions when x is p/6. In each case, use exact values.     3- sin…

A: Given expression is 3-sinx. If x=π6 then, 3-sinx=3-sinπ6=3-12…

Q: Cos x d.x 5. (1+ sin æ)5 6. csc (2x + 1) cot(2x + 1) dæ

A: The given integral is5.∫cos x(1+sinx)5dx6.∫csc3(2x+1)cot(2x+1)dx

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: (6) For each statement below, determine whether the equality is correct, and explain your solution.…

A: (a) Consider the given equation: sinsin-1x=x This is true for all the function values because domain…

Q: Let x = 30 0 and y = 45 0 in each of the expressions that follow,and then simplify each expression…

A: Consider the following values: x=30°y=45° Consider the following expression:…

Q: For the expression that follows, replace x with 30° and then simplify as much as possible. −5 sin…

A: Given : The replace x with 30° and then simplify as much as possible,          = -5 sin(2x)…

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

A: The given expression is 6cosx .

Q: The number of hours of daylight in Boston is given by:where x is the number of days after January…

A: Relation given - y = 3sin2π365x-79+12where,y = number of hoursx = number of daysGiven that,   y =…

Q: Find the values of the following. 1. sin(4 + 7j)

A: We have to evaluate sin( 4+7j)  sin(a+bj)=sin a cosh b+j cos a sinh b ⇒sin(4+7j)=sin 4 cosh 7+j cos…

Q: Evaluate the following expression when x is π/6. Use exact values. 4 − 2/3  sin(3x − π)

A:

Q: 2. Evaluate the following expressions, using a calculator if necessary: a. tan 46° b. sin 49°12' c.…

A: To calculate the following values

Q: Evaluate the following expression. sin?(4) 1/2 3/4

A: put the value and solve

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: Find the exact value of sin ) given csc(x) = 8, %3D for 90° < x< 180°. 317 А. 2. С. 2 16 + 12 D. 317…

A: Given that csc(x)=8 for 90°&lt;x&lt;180° ⇒sin(x)=1csc(x)⇒sin(x)=18 Since…

Q: TT Solve sin ( – x) - sin (x +) = 1 for 0 <x < 2 T 4

A: We have to solve for x

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

A:

Q: For the expression that follows, replace x with 30° and then simplify as much as possible. −7 sin…

A: Given  -7 sin 2xwe find the value of -7 sin 2xif replace x with 30°

Q: find all values of x, 0 &lt;= x &lt;=  2p, forwhich the following are true:   sin x = 1

A: To find the value of x.

Q: Solve the following. sin? (G) + cos?x = 1 where x E [0, 2n)

A: Solve  sin2(x/2) +cos2x = 1 .....(1)

Q: If P = A sin 0 + B cos 0 and Q = A cos 0- B sin 0, find the value of A2 + B² in terms of P and Q. А.…

A:

Q: B b C If m/C= 90° and m⁄A = 35°, one would use sin A to find the value of b. Select one: True False…

A:

Q: 61 11 60 L Which is art equivalent expression for sin K?

A: A triangle is a polygon having three sides and three vertices. Sum of interior angles of triangle is…

Q: Evaluate the following expressions. Enter exact answers using fractions. 12 sin cos 13 :)) -D -1 tan…

A: Given, sincos-1-1213 tansin-1-45 We have the evaluate the expression and write the exact values.

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 expression of y= sin In(5x +2) equal to du? * O 5/5x + 2 O In 5x + 2 O 1

A: We have to find the value of du.

Q: The expression D (sin x) is equal to sin ( x + 2 O True False

A: An inflection point is a point on the graph of a function at which the concavity changes. At the…

Q: Simplify the expression vx+S1 as much as possible after substituting 9 tan 6 for x. 9 cos e | 9 csc…

A:

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: Show that sin (A + B) is not, in general, equal to sin A + sin B by substituting 30 degree forA and…

A: To prove: sin (A + B) is not, in general, equal to sin A + sin B Given information: The value of A…

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

A:

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

A:

Q: Find the exact value of the following expression. V3 1 sin | 2

A:

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

A:

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

A:

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: Complete the following table using exact values. (If an answer is undefined, enter UNDEFINED.) sin x…

A: The sin value for given angles, we have to find the cosec values.

Q: Given sin (a) 12 and 270° < a < 360°, find the exact values of 13 sin (을). A) _ 4 V13 B) _ 2 V13 -…

A:

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.