10. (a) Define the inverse sine function, the inverse cosine func- tion, and the inverse tangent function. (b) Find sin- cos and tan-1. 2 (c) For what values of x is the equation sin(sinx) = x true? For what values of x is the equation sin-(sin x) = x true?

Q: |1-cos(0) If tan 0 > 0 and cos 0 < 0, sin = - 2

A:

Q: Is sin-1 x the same thing as1/sin x?

A:

Q: 13. If tan(x) = 3/2 and cos x <0, find the exact value of sec x. %3D

A: Given, tanx = 3/2  cos x &lt; 0   We have to find sec x

Q: 2. A ball travels in a circle at 3 radians/s and starts on the positive x-axis. How far away is the…

A: Let 'w' be the angular speed of the ball travels in a circle.  Thus, w= 3 radians/s.  Let 't' be the…

Q: Reduce sin 0 to an expression involving only function of multiples of 0, raised to the first power.

A: Given, sin4θ  We have to reduce sin4θ to an expression involving only function of multiples of θ,…

Q: 8. Find the exact value. sin(tan¬1 x)

A: Convert tan-1x into sin-1x then calculate exact value

Q: 8. Find the exact value of 2 sin (tan-1 ()

A: Let's find.

Q: if sinh x=-1/2 then coth x is

A:

Q: Find the period and amplitude of the function. 2n y=-4 sin x- 3 Give the exact values, not decimal…

A: If y=AsinBx is a function then its amplitude is A and its period is 2πB.   The given function is…

Q: Find the equation of the tangent line of the inverse sin function at the point (1/2,pi/6)

A:

Q: cos x csc3 x + C sin4 x 1.

A: To evaluate the given integral.

Q: How can the graph of y = sin-1 x be obtained from the graph of the restricted sine function?

A: given: y=sin-1x

Q: 1 1+ cos x 9. 1- cos x || sin? |

A: We can verify the statement as below.

Q: value of cos x is given. Find sin x and 3T xET, 15 X= 17'

A:

Q: Graph the equation for values of x between 0 and 720 In multiples of 30. y =5 sin(x)

A: Period of y=5sin(x) is 360 degree So between 0 to 720 degree, there are 720/360= 2 periods So we…

Q: Find the derivative of tan−¹(x).If you use the identity 1 + tan²(x) = sec²(x), you can write the…

A:

Q: a) sin ) co () - c) tan 4) cot (- *) - ) me (- *) - sec

A:

Q: 7. Find the amplitude and period for the function y = -3 sin(4x).

A: Given,           The function is y=-3sin4x .

Q: 7. csc'x - cotx + tan'x CoSx - sin?xcosx

A:

Q: (³² sin æcosx tan³ xcot³ x sec xcscx dx

A:

Q: (b) Use the graph of cos x to determine where cosx is positive and where it is negative. (c) Explain…

A:

Q: Find sin x if sin x – cos x x = 3 sec x

A: Consider the given trigonometric expression, sinx-cosx=13 now square both side of the equation,…

Q: Find an equivalent expression for sin 4x in terms of function values x sin 4x =

A: power series of f(x) about x =a is  f(x) = ∑h=0∞ fn(a)n! (x-a)n ------- (*)

Q: 86. Use the quotient rule and the derivatives of the sine and cosine functions to prove that (cotx)…

A: prove that ddx(cot x) = - csc2x

Q: The simplified form of [csc(-x) + cos(-x)] · [9 sin² æ sec? æ]

A: The simplified form of [csc(-x) + cos(-x)] [9 sin²x sec² x]

Q: Find sin x if cot x=-(√3)/2 and cos x (less than) 0

A: We will find the value of sin x.

Q: If x is in radians, the derivative of sin(x) is cos(x). Find the derivative of sin(x) when x is in…

A: Given, sinx°  We have to find the derivative of  sinx°.

Q: 6. When defining the inverse sine function, the domain of y = sin x is restricted to -÷<xs. a. Why…

A:

Q: 4л coS 씀Cos 즙Cs -sin sin 15 15 15

A: We have to find the exact value cosπ15cos4π15-sinπ15sin4π15.

Q: 7.6, #1 Find the exact value of the expression whenever it is defined. sin- (-) = b. tan-(-V3) =

A:

Q: Find the amplitude, period, and phase shift of the function. y = 5 + 3 sin 6(x + 3) and  than graph…

A:

Q: Find a value of x that satisfies the equation sin (-84°) = cos (x). %3D

A: To find: The value of x. Given: The equation sin-84°=cos x. Concept used: sin-θ=-sin θ sin3π2-x=-cos…

Q: Find the exact value of the expression whenever it is defined.

A: Given:a sinsin-1513- cos-1-35b cossin-145+tan-134c tancos-112- sin-1 -12

Q: 9. cos(x-)

A:

Q: 4. Find the exact value of sin if cose 2 3 and e is in QIII. cose =-- |

A: According to question,Given conditions,cos θ = -35,θ is in third quadrant.

Q: 1- (sin (Cos(2x)+Cos (sinc2x)

A: Given derivative

Q: 10. Solve the equation for x if 0 < x < 2n. 2 sin x - cot x = csC X

A:

Q: what is the equation of the tangent line to the function f(x)=2 sin x + cos x at x=pi /4 ( express…

A:

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

A:

Q: Find the exact function value. 3n sin 4

A: We have to find the exact function value for sin-3π4.

Q: The inverse cosine function has a domain of [-1,1] and a range of [0,- ]. The inverse tangent…

A: Given the data

Q: , given tan x = -4 and cos x < 0

A: Given that tan x and cos x both have negative values , So, the value of x must lies in 2nd quadrant…

Q: = cos 30 + sin? tan 2x 1-cot 2x = 2 csc(1 – 3x)

A: Find the first derivative: 7. y=log sin xa 8. y=e3x 9. y=e-bcos 2b

Q: 5) Find the exact value of cos [tan--si sin-" (-): 12

A:

Q: Find exact function values for: a. sin(α/2) b. cos(α/2) c. tan (α/2) cosα = 12/13, (3π)/2 < α <…

A: The given trigonometric ratio is cosα=1213 ,where3π2&lt;α&lt;2π (a) To find the value of sinα2…

Q: If y = -sin x, what x-value corresponds to a y-value of -1 between 0 and 27? 2 -1 ?

A:

Q: Find sin (x- π/2) if cos x=0.65

A: On solving this we will get

Q: Find sin 0 and tan 0 if the terminal side of 0 lies along the line y = -7x in QII. sin 0 = tan 0:

A: Given that terminal side of ϑ lies along the line y = -7x. Note that the slope of the line y = -7x…