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

$sin(theta)=-3/5$

From the pythagorean trigonometric identity

$1+cot^2(theta)=csc^2(theta)=>csc(theta)=+-sqrt(1+cot^2(theta))$

For $cot(theta)=-4/3$

$csc(theta)=+-sqrt(1+(-4/3)^2)=+-sqrt(1+16/9)=+-5/3$

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

$csc(theta)=-5/3$

By the definition of cosecant, sine must be

$sin(theta)=1/csc(theta)=1/(-5/3)=-3/5$