Question

1) Completely simplify

2) Write the expression cot( in terms of x and y only

3) If csc x = 2 and x is in Q I, determine the exact values of sin x and cos x.

4) Use a sum to product formula to rewrite sin 2x – sin 5x as the product of two trig functions.

Step by Step please

5) Use a product to sum formula to rewrite sin(2x) * sin(5x) as a sum of two trig functions.

Answer #1

Name the Quadrant
1. cot q = -3 , tan q =
2. cot q = -3 , tan q =
3. sec q = 1.5 , cos q =
4. cos q = -3/5 , sec q =
Solve the identity function
1. tan x / sin x
2. cos t / cot t
3. cos a csc a tan a
4. cot t sec t sin t
5. 1 - cos2 q
6. csc2 q - 1
7....

Differentiate the following functions. Do not simplify
k(x) = ln(cot(x))
L `(x) = 4 csc-1(x2)
m(x) = sin(x) / cosh(x)
n(x) = 2 tanh-1(x4 + 1)

1.Find all solutions on the interval [0, 2π)
csc (2x)-9=0
2. Rewrite in terms of sin(x) and cos(x)
Sin (x +11pi/6)

Consider the following expression: 3sinh(x) - 2cosh(x)
[a] Write the expression in terms of exponential functions, then
completely simplify it.
Note: Your final answer can't use any hyperbolic functions
[b] Using the answer from [a], solve the equation 3sinh(x) -
2cosh(x) = 3
Note: Your work leading to the final answer cannot use any
inverse hyperbolic functions

find the amplitude of y= -4 sin (3x + pie).
find the period of y= 3csc 2/3 x
find the phase shift of the function y= -5 sin (2x -
pie/2)
find the exact value of the real number y. Use radian measure
y= csc^-1 (2).
give the degree measure of theta use trig chart. theta = cos
^-1 (square root 2/2)
use a calculator to give the value in degrees. sin^-1
(-0.4848)
use a calculator to give the real...

1. Differentiate the following functions. Do not simplify.
(a) f(x) = x^7 tan(x)
(b) g(x) = sin(x) / 5x + ex
(c) h(x) = (x^4 + 3x^2 - 6)^5
(d) i(x) = 4e^sin(9x)
(e) j(x) = ln(x) / x5
(f) k(x) = ln(cot(x))
(g) L(x) = 4 csc^-1 (x2)
(h) m(x) = sin(x) / cosh(x)
(i) n(x) = 2 tanh^-1 (x4 + 1)

1. Use the given conditions to find the exact value of the
expression.
sin(α) = -5/3, tan(α) > 0, sin(α - 5π/3)
2. Use the given conditions to find the exact value of the
expression.
cos α = 24/25, sin α < 0, cos(α + π/6)
3. Use the given conditions to find the exact value of the
expression.
cot x = √3, cos x < 0, tan(x + π/6)
4. If α and β are acute angles such that...

Find the derivative of the functions
y=cot-1(1/x^2+1)
y=(cos-1x)^2
y=tan-1(x^2sinx^3)
y= In(1/1+x^2)
y=(In(1+x^5))^2
y=(cos(x^2+1)^7

Math 163 April 28th.
1) Consider the function ?(?) = ? 2? 3?. Write the first three
non-zero terms of the following series, and find a series
formula:
a. the Maclaurin series of ?(?).
b. the Taylor series of ?(?) centered at ? = −2.
2) Consider the function ?(?) = ? arctan(3?). Write the first
three non-zero terms of the following series, and find a series
formula:
a. the Maclaurin series of ?(?).
b. the Taylor series of ?(?)...

13. Consider
f(x)=sqrt x-2
a) Using any of the three limit formulas to find f ′ ( a
), what is the slope of the tangent line to f ( x )at x = 18? (6
points execution, 2 points notation)
b) Find the equation of the tangent line at x =
18
14. State the derivative.
a) d/ d x [ x ^n ]
b) d /d x [ cos x ]
c) d /d x [ csc...

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