Question

Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90∘.

Answer 1

Convert Ф = 90°, 45°, 0°, -45°, -90° into radans to obtain
Ф = π/2, π/4, 0, -π/4, -π/2 rad.

The given function is
v = 100 cos(ωt + Ф)

Create the following tables.
We shall use
ωt : 0 π/2 π (3/2)π 2π

Ф = π/2
ωt+Ф : π/2 π (3π)/2 2π (5π)/2
v : 0 -100 0 100 0

Ф = π/4
ωt+Ф : π/4 (3/4)π (5/4)π (7/4)π (9/4)π
v : 70.7 -70.7 -70.7 70.7 70.7

Ф = 0
ωt+Ф : 0 π/2 π (3/2)π 2π
v : 100 0 -100 0 100

Ф = -π/4
ωt+Ф : -π/4 π/4 (3/4)π (5/4)π (7/4)π
v : 70.7 70.7 -70.7 -70.7 70.7

Ф = -π/2
ωt+Ф: -π/2 0 π/2 π (3/2)π
v : 0 100 0 -100 0

Sketches of graphs for the different cases are shown below.