Answer:
√3
Step-by-step explanation:
To recall trigonometric ratios, there is a special acronym known as sohcahtoa which stands for
- sin(x)=opposite/ hypotenuse
- cos(x)=adjacent/hypotenuse
- tan(x)=opposite /hypotenuse
Finding the angle [tex]\theta[/tex]
We are given that,
[tex] \displaystyle \sin( \theta) = \frac{ \sqrt{3} }{2} [/tex]
To find the angle [tex]\theta[/tex] , take inverse of sin of both sides,
[tex] \displaystyle { \sin}^{ - 1}( \sin( \theta) )= { \sin}^{ - 1} \bigg(\frac{ \sqrt{3} }{2} \bigg )[/tex]
with the help of unit circle,we acquire:
[tex] \displaystyle \boxed{\theta= {60}^{ \circ} }[/tex]
Finding [tex]\tan\theta[/tex]
simply plug in the value of theta:
[tex] \tan( {60}^{ \circ} ) [/tex]
using unit circle,we get:
[tex] \implies \tan( {60}^{ \circ} ) = \boxed{\sqrt{3} }[/tex]
and we're done!
