Exam 16: Trigonometric Models

Use the addition formulas: (x+y)=x\cdoty+x\cdoty (x-y)=x\cdoty-x\cdoty (x+y)=x\cdoty-x\cdoty (x-y)=x\cdoty+x\cdoty To calculate $\cos \left( \frac { \pi } { 3 } \right)$ , given that $\sin \left( \frac { \pi } { 6 } \right) = \frac { 1 } { 2 }$ and $\cos \left( \frac { \pi } { 6 } \right) = \frac { \sqrt { 3 } } { 2 }$ .

Find the derivative of the function. $g ( x ) = 9 \sin ( x ) \cdot \tan x$

Evaluate the integral. $\int ( 10 x + 25 ) \sin \left( x ^ { 2 } + 5 x \right) \mathrm { d } x$

Find the derivative of the function. $z ( x ) = 3 \ln \mid 4 ( \sec x + \tan x )$

Sales of computers are subject to seasonal fluctuations. Computer City's sales of computers in 1995 and 1996 can be approximated by the function $s ( t ) = 0.468 \sin ( 1.25 t + 1.73 ) + 0.79 ( 1 \leq t \leq 6 )$ Where t is time in quarters ( $t = 1$ represents the end of the first quarter of 1995) and $s ( t )$ is computer sales (quarterly revenue) in billions of dollars. Estimate Computer City's maximum and minimum quarterly revenue from computer sales.

Model the curve with a sine function. ​ ​ ​ Note that the period of the curve is $P = 0.4$ and its range is $[ - 4 , - 2 ]$ . Write the model function as a function of x and π.

Find the derivative of the function. $t ( x ) = \frac { \cot x } { 4 + 8 \sec x }$