115k views
5 votes
An angle θ terminates in quadrant II. If tan θ = - squareroot3, determine the value of sin θ.

1 Answer

4 votes
we know the angle is in the II quadrant, therefore the adjacent side or cosine is negative and the opposite side or sine is positive there.


\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad \qquad tan(\theta)=\cfrac{opposite}{adjacent}\\\\ -------------------------------\\\\ tan(\theta )=-√(3)\implies tan(\theta )=\cfrac{\stackrel{opposite}{√(3)}}{\stackrel{adjacent}{-1}}\qquad \begin{array}{llll} \textit{let's find the }\\ hypotenuse \end{array} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=√(a^2+b^2)\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}


\bf c=\sqrt{(-1)^2+(√(3))^2}\implies c=√(1+3)\implies c=√(4)\implies c=2\\\\ -------------------------------\\\\ sin(\theta)=\cfrac{opposite}{hypotenuse}\qquad \qquad sin(\theta)=\cfrac{√(3)}{2}
User Kishikawa Katsumi
by
7.7k points

Related questions

asked Mar 1, 2018 132k views
MarcE asked Mar 1, 2018
by MarcE
7.8k points
1 answer
4 votes
132k views
asked Aug 10, 2021 24.9k views
Jlvaquero asked Aug 10, 2021
by Jlvaquero
8.0k points
2 answers
4 votes
24.9k views
asked May 10, 2017 214k views
Flaashing asked May 10, 2017
by Flaashing
7.7k points
1 answer
4 votes
214k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories