If cot⁡θ=−3 and secθ&lt;0 Find sin⁡θ

Given that cot⁡θ=−3&lt;0 and sec⁡θ then θ is in QII so sin⁡θ&gt;0. since cot⁡θ=−3=−31 we can let adj =3 and opp =1 opp2+adj2=hyp2 (1)2+(3)2=hyp21+3=hyp2 4=hyp2 hyp=2 So, sin⁡θ=opphyp since sin⁡θ&gt;0 sin⁡θ=12

Expert answers to "If cot⁡θ=−3 and secθ<0 Find sin⁡θ"

High School
Geometry
Trigonometry
Right triangles and trigonometry

Tammy Todd

Answered question

2021-01-31

If $\cot θ = - \sqrt{3} and s e c θ < 0$
Find $\sin θ$

Answer & Explanation

Nola Robson

Skilled2021-02-01Added 94 answers

Given that $\cot θ = - \sqrt{3} < 0 and \sec θ then θ is in QII so \sin θ > 0$ .
since $\cot θ = - \sqrt{3} = \frac{- \sqrt{3}}{1} we can let adj = \sqrt{3} and opp = 1$
$o p p^{2} + a d j^{2} = h y p^{2}$
$(1)^{2} + (\sqrt{3})^{2} = h y p^{2}$ $1 + 3 = h y p^{2}$
$4 = h y p^{2}$
$h y p = 2$
So, $\sin θ = \frac{o p p}{h y p}$
since $\sin θ > 0$
$\sin θ = \frac{1}{2}$

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