Question

Given cos theta = √3/4 and sin theta < 0. What is the value of sin theta? ​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

• sin²x + cos²x = 1 ⇒ sin x = ± $\sqrt{1-cos^2x}$

Since sinΘ < 0 , then

sinΘ = - $\sqrt{1-(\frac{\sqrt{3} }{4})^2 }$

       = - $\sqrt{1-\frac{3}{16} }$

      = - $\sqrt{\frac{13}{16} }$ = - $\frac{\sqrt{13} }{4}$

Answer 2

Answer:

$\sqrt{ \frac{13}{16} }$

Step-by-step explanation:

$cos \: theta = \frac{ \sqrt{3} }{4} \\ sin \: theta = \sqrt{1 - {cos}^{2} theta} \\ = \sqrt{1 - {( \frac{ \sqrt{3} }{4} ) }^{2}} \\ = \sqrt{1 - \frac{3}{16}} \\ = \sqrt{ \frac{13}{16} }$