Answer:
cosθ = - [tex]\frac{\sqrt{33}}{7}[/tex].
Step-by-step explanation:
Given : sinθ=[tex]\frac{4}{7}[/tex].
To find : What is the exact value of cosθ in simplified form .
Solution : We have given sinθ=[tex]\frac{4}{7}[/tex].
By the trigonometric identity : [tex](sin)^{2} +(cos)^{2} = 1[/tex].
Plug the value of sinθ=[tex]\frac{4}{7}[/tex].
[tex](\frac{4}{7}) ^{2} + cos^{2} = 1[/tex].
[tex](\frac{16}{49}) + cos^{2} = 1[/tex].
Subtracting [tex]\frac{16}{49}[/tex] from both sides
[tex]cos^{2} = 1 - \frac{16}{49}[/tex].
[tex]cos^{2} = \frac{49 -16}{49}[/tex].
[tex]cos^{2} = \frac{33}{49}[/tex].
Taking square root both sides
[tex]cos ( theta) = \sqrt{\frac{33}{49} }[/tex].
cosθ = ± [tex]\frac{\sqrt{33}}{7}[/tex].
θ lies in Quadrant II so, cosθ = - [tex]\frac{\sqrt{33}}{7}[/tex].
Therefore, cosθ = - [tex]\frac{\sqrt{33}}{7}[/tex].
