Which expressions are equivalent to −tan⁡ θ?

Question

1) Which expressions are equivalent to −tan⁡ θ?

There may be more than one correct answer. Select all that apply.

a) 1/cot(−θ)

b) 1/cotθ

c) tan θ

d) −1/cotθ

e) −1/cot(−θ)

f) tan(−θ)

2) What is the correct way to apply the Sum Identity to find sin105∘?

a) sin105º=sin(45º+60º)=sin(45º)sin(60∘)+cos(45º)cos(60º)

b) sin105º=sin(45º+60º)=sin(45º)cos(60º)−cos(45º)sin(60º)

c) sin105º=sin(45º+60º)=sin(45º)cos(60º)+cos(45º)sin(60º)

d) sin105º=sin(45º+60º)=sin(45º)sin(60º)−cos(45º)cos(60º)

Answer 1

Hi Judite S.,

1) For each of the trigonometric functions use the Formulas For Negatives and Fundamental Identities to solve:

a) 1/cot(-θ) = 1/-cot(θ) = - tan(θ), [cot(-θ) = -cot(θ) {Formula for negatives}; cot(θ) = 1/tan(θ), {Fundamental Identities} which can be rearranged to tan(θ) = 1/cot(θ)]

See if you can do the rest. [a, d, and f are correct].

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2) Apply the Addition Formula: sin( u + v ) = sin(u)cos(v) - cos(u)sin(v).

sin(105^o) = sin(45^o + 60^o) where u = 45^o and v = 60^o.

sin(105^o) = sin(45^o)cos(60^o) - cos(45^o)sin(60^o)

We have a minus sign, so a and c are not correct. That leaves b and d. Can you see which one it is?

I hope this helps, Joe.