Exam 8: Trigonometric Identities and Equations

Use the fundamental identities to find the value of the trigonometric function. -Find $\cot \theta$ if $\tan \theta = \frac { \sqrt { 7 } } { 3 }$ and $\theta$ is in quadrant III.

For the graph of a circular function y = f(x), determine whether f(-x) = f(x) or f(-x) = -f(x) is true. -

Factor the trigonometric expression and simplify. - $\tan ^ { 4 } x - \sec ^ { 4 } x$

Use identities to fill in the blank with the appropriate trigonometric function name. - $\sec 80^{\circ}=\frac{1}{.....10^{\circ}}$

Solve the problem. -Suppose that for an electrical appliance, voltage is given by $\mathrm { V } = 189 \sin 120 \pi \mathrm { t }$ and amperage by $\mathrm { I } = 1.07 \sin 120 \pi \mathrm { t }$ , where $\mathrm { t }$ is time in seconds. The wattage is given by $\mathrm { W } = \mathrm { VI }$ . Find the maximum wattage used by the appliance.

Use Identities to find the exact value. - $\cos \left( - 165 ^ { \circ } \right)$

Use a sum or difference identity to find the exact value. - $\sin 255 ^ { \circ } \cos 15 ^ { \circ } - \cos 255 ^ { \circ } \sin 15 ^ { \circ }$

Use a sum or difference identity to find the exact value. - $\frac { \tan \frac { \pi } { 15 } + \tan \frac { 4 \pi } { 15 } } { 1 - \tan \frac { \pi } { 15 } \tan \frac { 4 \pi } { 15 } }$

Solve the equation for solutions over the interval [0, $[ 0,2 \pi )$ ). Write solutions as exact values or to four decimal places, as appropriate. -It can be shown that if the angle of elevation from an observer to the top of an object is A and the an; elevation $\mathrm { d } \mathrm { ft }$ closer is $\mathrm { B }$ , then the height of the object is given by $\mathrm { h } = \frac { \mathrm { d } } { \cot \mathrm { A } - \cot \mathrm { B } } \mathrm { ft }$ . Find $\mathrm { A }$ if $\mathrm { h } = 40 \mathrm { ft } , \mathrm { d } = 30 \mathrm { ft }$ , and $\mathrm { B } = 39 ^ { \circ }$ . Give your answer in degrees to the nearest hundredth.

Solve the equation for exact solutions. - $6 \cos ^ { - 1 } x = \pi$

Solve the equation for exact solutions. - $\cot ^ { - 1 } x + \cot ^ { - 1 } ( 1 + x ) = \frac { \pi } { 4 }$

Factor the trigonometric expression and simplify. - $\sec ^ { 4 } x + \sec ^ { 2 } x \tan ^ { 2 } x - 2 \tan ^ { 4 } x$

Verify that the equation is an identity. - $\frac { \sin ( \alpha - \beta ) } { \sin \alpha \sin \beta } = \cot \beta - \cot \alpha$

Solve the equation for solutions over the interval [0, $[ 0,2 \pi )$ ). Write solutions as exact values or to four decimal places, as appropriate. - $\tan 2 x + \sec 2 x = 2$

Use a calculator to find the value. Give answers as real numbers and round to 4 decimal places, if necessary. - $\cot ( - \arcsin \pi )$

Factor the trigonometric expression and simplify. - $\sin ^ { 2 } x + \sin ^ { 2 } x \cot ^ { 2 } x$

Express the function as a trigonometric function of x. - $\tan 4 x$

Express the function as a trigonometric function of x. - $\sin 3 x$

Complete the sentence so the result is an identity. Let x be any real number. - $- ^ { + \sin ^ { 2 } x = 1 }$

Complete the sentence so the result is an identity. Let x be any real number. - $- ^ { + \tan ^ { 2 } x = \sec ^ { 2 } x }$