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. (no labels and no approximations).

f(x) = $e ^ { x ^ { 3 } }$ ∙ tan 2x Enter your answer without parentheses except as indicated in this form, $\mathrm { e } ^ { \mathrm { P } } ( \mathrm { x } )$ (ab + 2d).

f(x) = 2 sec x Enter your answer without parentheses, secants before tangents in terms, no labels.

Refer to the triangle whose sides and angles are labeled below. Estimate t if a = 24, b = 10, and c = 26. Enter just a real number rounded to one decimal place.

Determine the value of cos t when t = -7π.

Convert the given angle to degree measure. - $\frac { 9 \pi } { 2 }$

Convert 327° to radian measure.

Integrate - $\int _ { 0 } ^ { 1 } \sec ^ { 2 } \left( \frac { \pi x } { 4 } \right) d x$

Convert the given angle to degree measure. -10°

Differentiate. - $\frac { \sin x } { x }$

$\int _ { 0 } ^ { \pi / 2 } \sec ^ { 2 } \left( x + \frac { \pi } { 4 } \right)$ dx Enter just an integer.

Find the area under the curve y = sin(3t - π) for $\frac { \pi } { 3 }$ ≤ t ≤ $\frac { 2 \pi } { 3 }$ . Enter just a reduced fraction.

Find the slope of the line tangent to the graph of y = $\cos ^ { 2 }$ 4t at t = $\frac { \pi } { 3 }$ . Enter just a $\sqrt { b }$ .

f(x) = tan(3x) sin x Enter your answer without parentheses, no labels, any term containing sine appearing first.

Suppose sin t = - $\frac { 5 } { 13 }$ and cos t is negative. What is cos t?

Convert the given angle to degree measure. -760°

Differentiate. -f(x) = $( \sin x + \cos x ) ^ { 5 }$

$\cos ^ { 2 }$ x $\sin ^ { 3 }$ x Enter cosine before sine in all terms, no parentheses around the arguments.

Find the indefinite integral. - $\int \cos ( 2 x + 1 )$ dx

A department store has revenue from the sale of electrical kitchen appliances that is given approximately by $R ( t ) = 2.2 + 2.2 \cos \frac { \pi t } { 23 }$ for 0 ≤ t ≤ 52, where R(t) is revenue in hundreds of dollars for a week of sales t weeks after January 1. What is the total revenue (to the nearest hundred dollars) earned from t = 10 to $t = 16 ?$