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#