Answer:
- sin(θ) = -(4√15)/17
- cos(θ) = 7/17 . . . . . . . given
- tan(θ) = -(4√15)/7
- csc(θ) = -(17√15)/60
- sec(θ) = 17/7
- cot(θ) = -(7√15)/60
Step-by-step explanation:
The relationship between sine and cosine is ...
sin² + cos² = 1
Solving for sine gives ...
sin = ±√(1 -cos²)
In this problem, we want the negative root.
sin(θ) = -√(1 -(7/17)²) = -√(240/289) = -(4√15)/17
tan(θ) = sin(θ)/cos(θ) = ((-4√15)/17)/(7/17) = -(4√15)/7
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And the inverse functions are ...
sec(θ) = 1/cos(θ) = 17/7
csc(θ) = 1/sin(θ) = -17/(4√15) = -(17√15)/60
cot(θ) = 1/tan(θ) = -(7√15)/60
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Of course, you're aware that 1/√15 = (√15)/15.
