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# EG3007 Engineering Analysis And Methods 1 0 Download1 Pages / 37 Words

## Question:

### Learning Outcomes:

Analyse and model engineering situations and solve problems using trigonometric methods.

Analyse and model engineering situations and solve problems using complex number and phasor diagram methods.

1. FIGURE 1 shows the positions of four towns marked on a map. • Calculate, to the nearest kilometre, the distance between towns Wand Y.
• Calculate, to the nearest degree, the size of the angle marked θ.
• Calculate, to the nearest kilometre, the distance between towns Yand Z.
1. The instantaneous value of current, iamp, at t seconds is given by:

i = 15 sin(100πt + 0.6)

### Find the value of

• The amplitude.
• The period.
• The frequency.
• The initial phase angle (when t= 0), expressed in both radians and degrees.
• The value of iwhen t = 2.5 s.
• The time (in milliseconds) when the current first reaches its maximum value.
1. Use the trigonometrical identities to expand and simplify if possible.
• (i)  cos(270° – θ)
• sin(270° – θ)
• cos(270° + θ)

(b) The voltage V1 and V2 are represented by as follows,

V1  = 3sin(ωt)

V2  = 2 cos(ωt)

If V3 is the sum of V1 and V2,

V3=V1+V2

Find the expression of V3 in sine waveform V3  = R sin(ω t + α )

and verify that the resultant voltage V3 is in the same frequency as V1 and V2.

1. (a) Given the equivalent impedance of a circuit can be calculated by the expression

Z = Z1Z2/Z1+Z2

If Z1 = 4 + j10 and Z2 = 12 – j3, calculate the impedance Z in both rectangular and polar forms.

• Three impedances are connected in parallel, Z1= 2 + j2, Z2 = 1 + j5 and Z3 = j Find the equivalent admittance Y

where: Express the admittance in both rectangular and polar forms.

1. The potential difference across a circuit is given by the complex number
• = 40+  j35 volts and the current is given by the complex number
• = 6+  j3 amps
• Sketch the appropriate phasors on an Argand diagram.
• Find the phase difference (i.e. the angle φ) between the phasors for voltage Vand the current I.
• Find the power (watt), given that

power = |V|  × |I|× cos( φ)

### Cite This Work

My Assignment Help. (2020). Engineering Analysis And Methods 1. Retrieved from https://myassignmenthelp.com/free-samples/eg3007-engineering-analysis-and-methods/trigonometric-methods.html.

My Assignment Help (2020) Engineering Analysis And Methods 1 [Online]. Available from: https://myassignmenthelp.com/free-samples/eg3007-engineering-analysis-and-methods/trigonometric-methods.html
[Accessed 28 October 2021].

My Assignment Help. 'Engineering Analysis And Methods 1' (My Assignment Help, 2020) <https://myassignmenthelp.com/free-samples/eg3007-engineering-analysis-and-methods/trigonometric-methods.html> accessed 28 October 2021.

My Assignment Help. Engineering Analysis And Methods 1 [Internet]. My Assignment Help. 2020 [cited 28 October 2021]. Available from: https://myassignmenthelp.com/free-samples/eg3007-engineering-analysis-and-methods/trigonometric-methods.html.

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