Question

1.Do you think a similar rule is true for cosine? That is, does –cos(θ) = cos(–θ)? Pick a value of θ and test this theory.

2. Using your example above, speculate on a rule that might be true for cos(-θ).

Answer 1

1.Do you think a similar rule is true for cosine? That is, does -cos (θ) = cos (-θ)? Pick a value of θ and test this theory.

It is not the same.
To prove it, let's choose a value of the angle:
θ = 45 degrees:
-cos (θ) = cos (-θ)
-cos (45) = cos (-45)
- (root (2) / 2) = (root (2) / 2)
answer:
NOT fulfilled: -cos (θ) = cos (-θ) (false)

2. Using your example above, speculate on a rule that might be true for cos (-θ).
cos (θ) = cos (-θ)
To prove it, let's choose a value of the angle:
θ = 45 degrees:
cos (θ) = cos (-θ)
cos (45) = cos (-45)
(root (2) / 2) = (root (2) / 2)
answer
A rule for cosine can be:
cos (θ) = cos (-θ)