Exam 9: Trigonometry

Hint: $a ^ { 2 } = b ^ { 2 } + c ^ { 2 }$ In the series circuit, if the impedance is 70 ohms and the reactance is 50 ohms, what is the value of the resistance? Round the answer to the nearer ohm.

What is the value of the resistance (R) in the series circuit shown? Carry the answer to two decimal places. $X _ { L } = \sqrt { Z ^ { 2 } - R ^ { 2 } }$

$E _ { i } = E _ { \max } \sin \theta$ Find the phase angle at which an instantaneous voltage of 144 appears in a wave with a peak value of 500 volts. Round the answer to the nearer degree.

$E _ { i } = E _ { \max } \sin \theta$ What is the maximum peak value of a 60-hertz wave that has an instantaneous voltage of 22 volts 1.67 milliseconds before the end of one cycle? Round the answer to the nearer tenth. $\theta = 360 t _ { i } f$

Hint: $a ^ { 2 } = b ^ { 2 } + c ^ { 2 }$ $X _ { L }$ = 400 ohms Z = 1,100 ohms Find R in ohms. Carry the answer to one decimal place.

$E _ { LI N E } = \sqrt { E_ R ^ { 2 } + E_ X ^ { 2 } }$ If the voltage across the reactance ( $E _X$ ) is 50 volts and the line voltage ( $E _ { \text {LINE } }$ ) is 300 volts, what is the voltage across the resistance ( $E _R$ )? Carry the answer to one decimal place.

If the resistance is changed to 40 ohms and ( $X _ { L }$ ) is the inductive reactance, what is the impedance (Z)? $X _ { L } = \sqrt { Z ^ { 2 } - R ^ { 2 } }$

$E _ { i } = E _ { \max } \sin \theta$ What is the magnitude of the voltage at point A? Express the answer to the nearer tenth.

Hexadecimal numbers that correspond to letters can be entered on the TI 36X calculator using the 3rd function key in conjunction with other keys that correspond to the letters A, B, C, D, E, and F.

$\theta = 360 t _ { i } f$ What is the time in milliseconds required to generate one cycle of voltage at 60 hertz?

Hint: $a ^ { 2 } = b ^ { 2 } + c ^ { 2 }$ In the circuit shown $E _ { C }$ is 135 volts and $E _b$ is 175 volts. Find $E _ { a }$ . Carry the answer to two decimal places.

$O P = V _ { 1 } ^ { 2 } + V _ { 2 } ^ { 2 } + 2 \left( V _ { 1 } \right) \left( V _ { 2 } \right) \cos \theta$ A transformer secondary circuit is shown. Find $I _ { S }$ . Express the answer to the nearer tenth. Hint: First apply Ohm s law E=IR to find $I _ { H }$ and $I _ { L }$ .

$\theta = 360 t _ { i } f$ What is the phase angle between two 60-hertz voltages generations separated by a time interval of three milliseconds? Carry the answer to one decimal place.

A TI 36X calculator is set in binary mode (BIN). The calculator display show 110100101. If the calculator is set to decimal (DEC) mode, what would the display show?

$O P = V _ { 1 } ^ { 2 } + V _ { 2 } ^ { 2 } + 2 \left( V _ { 1 } \right) \left( V _ { 2 } \right) \cos \theta$ Two voltages ( $E _ { 1 }$ and $E _ { 2 }$ ) are applied to a resister. $E _ { 1 }$ is 40 volts at $0 ^ { \circ }$ reference. $E _ { 2 }$ is 60 volts and leads $E _ { 1 }$ by $40 ^ { \circ }$ . Find $E_ R$ to the nearer tenth.

A TI 36X calculator is set in octal mode. The calculator display shows 116. If the calculator is set to hexadecimal mode, what would the display show?

Hint: $a ^ { 2 } = b ^ { 2 } + c ^ { 2 }$ Determine the voltage of $E _ { a }$ if $E _b$ is 105 and $E _ { C }$ is 120 volts. Carry the answer to two decimal places.

$E _ { i } = E _ { \max } \sin \theta$ An AC voltage has an instantaneous value of 110 volts. Find to the nearer degree the phase angle if the peak voltage is 155.5 volts.

$E _ { LI N E } = \sqrt { E_ R ^ { 2 } + E_ X ^ { 2 } }$ The line voltage ( $E _ { \text {LINE } }$ ) is 120 volts, and the voltage of the reactance ( $E_ X$ ) is 60 volts. What is the voltage across the resistance ( $E _R$ )? Carry the answer to two decimal places.

What is the output frequency to the nearer tenth hertz of a generator that produces two voltage waveforms in 5.55 milliseconds? Carry the answer to one decimal place. $f = 1 / t$