If cot(theta)=7, what is sin(theta), cos(theta), sec(theta) between 0 and 2 pi?

sanuluy 2020-11-12 Answered
If cot(θ)=7, what is sin(θ),cos(θ),sec(θ) between 0 and 2π?
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averes8
Answered 2020-11-13 Author has 92 answers

Draw a right-angled triangle ABC where B is 90 deg, A is θ.cot(θ)=ABBC=7.AC=72+1=52.AB=7,BC=1.
sin(θ)=BCAC=152=0.222=0.12=0.1414.
cos(θ)=752=1.422=0.72=0.9899.
sec(θ)=1cos(θ)=527=1.0102. These are all approximate values and apply to quadrant 1. cot(θ)=71 in quadrant 1, or 71 in quadrant 3. In this quadrant sin, cos, sec are all negative, so sin(θ)=0.1414,cos(θ)=0.9899,sec(θ)=1.0102 in QIII, and 0.1414, 0.9899, 1.0102 in QI.

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