Exam 8: The Trigonometric Functions

Give the values of tan t and sec t, where t is the radian measure of the angle shown. Enter just $a , b$ where a represents tan t and b represents sec t with any fractions reduced of form $\frac { \mathrm { c } } { \mathrm { d } }$ (no labels and no approximations).

Differentiate. - $( \sin 3 t ) ^ { 2 }$

f(t) = $( \sec 3 t ) ^ { 6 }$ Enter your answer without parentheses or labels, use a multiplication dot between the last two functions.

Find the slope of the tangent line to the graph of y = $e ^ { 3 x }$ cos $x ^ { 3 }$ at the origin. Enter just an integer.

Integrate - $\int \sec ^ { 2 } ( 1 - 2 x ) d x$

f(x) = $\csc ^ { 3 }$ x Enter your answer without parentheses, no labels, use the multiplication dot between functions of x.

Convert the given angle to degree measure. -15°

$\sin ^ { 3 }$ ( $x ^ { 3 }$ )Enter sine terms before cosine terms with parentheses around arguments.

$\sin ^ { 3 }$ (3t)Enter sines before cosines with parentheses around arguments.

Convert the given angle to degree measure. - $\frac { 2 \pi } { 3 }$

Determine the value of sin t and cos t when t = 3π. Enter your answer as just a, b where a represents sin t and b represents cos t (no labels)

f(x) = sec $x ^ { 2 }$ Enter your answer without parentheses or labels. Use the multiplication dot between the last two functions of x.

Differentiate. -x sin x

Find t such that 0 ≤ t ≤ $\frac { \pi } { 2 }$ and sin t = cos t.

Differentiate. - $\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { 3 \mathrm { x } } \tan \left( \mathrm { x } ^ { 2 } \right)$

The size of an animal population at time t is given by $\mathrm { N } ( \mathrm { t } ) = 50,000 + 200 \sin \frac { 7 \pi t } { 48 }$ , where t is the number of months from June 1, 1980. At what rate is the animal population changing on June 1, 1981? Enter your answer as a quotient reduced form $\frac { a } { b }$ with π in the numerator (no units).

f(t) = csc $t ^ { - 3 }$ Enter your answer without parentheses or labels. No multiplication dots. Enter your answer as a quotient leaving $t ^ { - 3 }$ in that form.

Convert the given angle to degree measure. - $\frac { 2 \pi } { 5 }$

Find the tangent line to the graph of f(x) = $( 1 + \sin x ) ^ { 3 }$ at $\left[ \frac { \pi } { 2 } , 8 \right]$ .

cos(cos x)Enter sines before cosines with parentheses around arguments and a multiplication dot between the first two terms.