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

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.