Trig Funtions

Question 1

d/dx sin(x)

Answer 1

cos(x)

Question 2

d/dx cos(x)

Answer 2

-sin(x)

Question 3

d/dx tan(x)

Answer 3

sec^2(x)

Question 4

d/dx csc(x)

Answer 4

-csc(x)cot(x)

Question 5

d/dx sec(x)

Answer 5

sec(x)tan(x)

Question 6

d/dx cot(x)

Answer 6

-csc^2(x)

Question 7

if you see something like √x + 1 or √x - 1

Answer 7

conjugate theory (multiply the numerator and denominator by the same thing) √x - 1

Question 8

. ______ ____
if given something like √x+h-2 - √x + 6

Answer 8

rememeber that
(√a + √b) (√a - √b) = a+b

Question 9

d/dx √x

Answer 9

x^(-1/2) or 1/(2√x)

Question 10

make sure you use ___ when doing velocity and physics problems

Answer 10

units

Question 11

use the marginal cost function to estimate the cost of manufacturing the 11th item

Answer 11

plug in 10 to the marginal cost function C’(10)

Question 12

find the actual cost of manufacturing the 11th item

Answer 12

C(11) - C(10)

Question 13

period =

Answer 13

2 pi / b

Question 14

difference between instantaneous and average velocity

Answer 14

The average rate of change gives a broad view of how the function behaves between two points and provides an overall slope between those points.
The instantaneous rate of change is more precise, providing the exact rate at a specific point and indicating how steep the curve is at that point.
Example: For a car’s journey, the average rate of change of position over a period is the car’s average speed, while the instantaneous rate of change is the speedometer reading at a particular instant.

The average rate of change is the slope of a straight line (secant) between two points on the function.
The instantaneous rate of change is the slope of the curve (tangent) at a single point.

Question 15

angle addition formula sin(a+b)

Answer 15

=sin a cos b + cos a sin b

Question 16

angle addition formula cos(a+b)

Answer 16

cos a cos b − sin a sin b