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).

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)