4. If tan 0 =E, x<0<, find the exact value of each of the following. 2' (a) sin (20) (b) cos (20) (c) sin 2 (d) cos 21 .... (a) sin (20) =

Q: Eliminate n from their equations  X= sin n + tan n and y=sin n - tan n

A: With the help of trigonometric identities we eliminate n from the equations.

Q: 20 What is the frequency of the periodic function f(0) =2 tan()? O 2 5 sin(-), What is the frequency…

A: Given f(θ) = 2 tan(2θ/3) Frequency of tan θ is 1 For f(θ) period is  π/(2/3) = 3π/2 Frequency is…

Q: 1. Use the trapezium rule to estimate the value of the following correct to four decimal places a) |…

A: 1a) It is required to estimate the value of ∫0π3tanxdx with 4 strip using trapezium rule.

Q: 3. Evaluate fe cos rdr 4. Evaluate: / tan -1 (3x)dx.

A:

Q: 4- Using the data sin(0.1) = 0.09983 and sin (0.2) = 0.19867, find an approximate value of sin…

A:

Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: 3. If cos x =- Find the sin x and tan x in the interval 13 XE

A: Given:        cosx=-513  we know that                      cosx=adjacenthypotenuse…

Q: 16. Calculate (sin 0 , 0 , cos 20) d0.

A: ∫0π&lt; sinθ,θ,cos 2θ&gt;dθ

Q: Evaluate sin (44°) + cos (29°) using differentials. Refer to special triangles.

A: To evaluate sin44°+cos29∘ using differentials.

Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin' x tan

A:

Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

Q: 口 | 1. What is the frequency of the periodic function 5 sin() f(x) = %3D 3.

A: Given Data: Equation: fx=5sin3θ49 ......1 The general equation of the sinusoidal function.…

Q: 23. x? sin (x³) cos (x³) dx

A: ∫x2sin5x3cos3x3dx=∫sin5x3cos3x3dx      x3=u,3x2dx=dx, x2dx=1/3 dx=∫sin5x3cos313dx

Q: 12 If sinh x= find cosh x, tanh x, coth x, sech x, and csch x. 35

A: Given, sinh x = 1235   We have to find  cosh x, tanh x, coth x, sech x  and  csc hx

Q: 7/2 S 3 cos (x) sin°(æ) dx =

A:

Q: If cos x is replaced by 1 - (x2/2) and |x |&lt;0.5, what estimate can be made of the error? Does 1 -…

A: We’ll answer the second question first. Notice the question have used first two digits of Maclaurin…

Q: -- cos( sin-!x) + C 1-x² A True B) False

A: SOLUTION-

Q: 2. Apply the properties of even and odd functions to find the exact va a. sin(-120°) (-#) c. sin…

A:

Q: Estimate the error if P2(x)= 1 - is used to estimate the value of cos x at x-0.7. Error - (Simplify…

A: to estimate the error

Q: 2x, given tan x= 2 and cos x is less than 0

A: Given tan x = 2 and cos x &lt; 0.

Q: what is y' of y=sin-1(cos x)

A:

Q: find the value of so that ky"=-1 at y=. 6. For cos x- sin y=-

A: On solving this by doing differentiation implicitly we get

Q: (B): Find the tangent equation to the curve y = sin² x at point x = 7. (C): Solve the following…

A:

Q: 2. Write –2 cos x – 3 sin x in the form R cos(x – a) with -7 < a < T. Round to three decimal places.

A: Answer is given in asked form.

Q: dr de sin - r- cos + eª cos = 0

A:

Q: 4. What is (Cos (x²)} dv 5. What is (tan x³) dx 6. What is (In x)7 dx

A: To find out the derivative.

Q: 19. Solve for x:x = (tan e + cote)² sin?e - tan?

A: Given that: x=(tanθ+cotθ)2sin2θ-tan2θ

Q: cos? (x) 5 x²e* 6 V1 – x³ 4 - ex 7 sinh(x) 8 x² arctan(x) 9 1- X

A:

Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

A:

Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin x tan 2. Given the…

A: We can solve the given problem as follows:

Q: b. Express tanh x in terms of e* and e-* and hence show that 2 tanh x tanh 2x = 1+ tanh? x' c. Given…

A: (b) To proof :   tanh2x=2tanhx1+tanh2x It is known that, sinhx=ex-e-x2coshx=ex+e-x2 so,…

Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

A:

Q: 1 and tan(t) > 0, find sin(t) and cos(-t) 3 If cos(t) sin(t) = cos(-t) =

A: Given:cost=-13sint=?cos-t=?Formula:sint=1-cos2tcos-t=cost

Q: 15 Find sin 2x, cos 2x, and tan 2x if cos.xr= and x terminates in quadrant IV. 17 sin 2x cos 2x !!…

A:

Q: 1- cos(0) (d) de sin (0)

A: We have to find integration

Q: If y=-cos x, what is x-value between pi and 2 pi corresponding to y-value of 1/2

A: Let's solve  for x value.

Q: 4. For x near zero it is possible to write tan x = 1+ 0(x") and tan x = 1 + o(x°). Find the values…

A:

Q: 1 COS 4 Now, differentiate f'(x) with respect to x. - 4 -x* sin(x4) f"(x) = -x°•si Submit Skip (you…

A:

Q: 2) Find the exact simplified value of tan 2, () 3m sin 0 where n s0<4 2.

A: Given

Q: Find the values of θ between 0° and 360° such that: sin θ = 0.8

A:

Q: 1. Match th A. Sin В. Cos С. Tan

A: As per the guideline i can answer only first question for you, more than one answer leads me towards…

Q: 4. y = Arc tan² x³ 5. Ø = Are cot 2x

A:

Q: If y=(1+x²) tan-x - x then y' is equal to

A:

Q: 18. The value of sin (7 +2) is equal to sin a cos z cos z - sin r

A: 18)

Q: 4. Use Gamma function to evaluate the integral: sin? (40) cos (20)d0.

A:

Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

A:

Q: 1 3. a) Verify that sin x cos x = tan x--- π for the value x =-. 4 Ls Sin 4cos 4 2.s TanT/4-Y2 しS…

A: We can use the concept of trignometrical ratio in order to solve the given problem.

Q: 12. Find the exact simplified function value of tan (2a). 4 where TTSAL 3T 2. Given sin a= -

A: