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.

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)