Find the Trigonometric value of cot θ = -4/3,270º < θ < 360º; sin θ ?

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Find the Trigonometric value of cot θ = -4/3,270º < θ < 360º; sin θ ?

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Answer 1 · 2018-02-19T09:54:56

$sin (θ) = - \frac{3}{5}$ $sin(theta)=-3/5$

Explanation:

From the pythagorean trigonometric identity

$1 + {cot}^{2} (θ) = {csc}^{2} (θ) \Rightarrow csc (θ) = \pm \sqrt{1 + {cot}^{2} (θ)}$ $1+cot^2(theta)=csc^2(theta)=>csc(theta)=+-sqrt(1+cot^2(theta))$

For $cot (θ) = - \frac{4}{3}$ $cot(theta)=-4/3$

$csc (θ) = \pm \sqrt{1 + {(- \frac{4}{3})}^{2}} = \pm \sqrt{1 + \frac{16}{9}} = \pm \frac{5}{3}$ $csc(theta)=+-sqrt(1+(-4/3)^2)=+-sqrt(1+16/9)=+-5/3$

When $270^{\circ} < θ < 360^{\circ}$ $270^@< theta <360^@$ the angle must be in the 4. quadrant, therefore cosecant is negative

$csc (θ) = - \frac{5}{3}$ $csc(theta)=-5/3$

By the definition of cosecant, sine must be

$sin (θ) = \frac{1}{csc (θ)} = \frac{1}{- \frac{5}{3}} = - \frac{3}{5}$ $sin(theta)=1/csc(theta)=1/(-5/3)=-3/5$

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Find the Trigonometric value of cot θ = -4/3,270º < θ < 360º; sin θ ?

1 Answer

Explanation:

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