Task 1

In this task, you will understand the use of trigonometric functions.

Scenario: A complex voltage is usually represented by the waveform expressed in trigonometric function. The waveform of voltage representing the input voltage in the circuit by the expression in sinusoidal waveform as v = 3 sin ωt + 5 cos ωt as an analogue circuit. The voltage has the frequency ω.

Task 1.1 (P1.1)

If v = 3 sin ωt + 5 cos ωt in the form R sin (ωt +alpha ) to perform

i. Sketch graphs of the waveform on the axes

ii. Explain the meaning of R, ω and alpha.

Task 1.2 (P1.2)

a) The value of voltage in an AC circuit at any time t second is given by above waveform R sin (ωt +alpha ), determine:

i) The amplitude, period, frequency and phase angle (in degrees)

ii) The value of the voltage when t=0

iii) The value of the voltage when t=10ms

iv) The time when the voltage first reaches 300V

b) The conversion of a sinωt + b cosωt into R sin(ωt +alpha ) to prove the sine and cosine function of the same frequency added produce a sine wave of the same frequency.

Task 1.3 (P1.3)

Evaluate the following problems using trigonometric identities to prove that:

Verify the above identities using the numerical values.