Question

The angle lies in Quadrant II. sin0=3/4 What is cos 0?

Answer 1

Answer:

cosФ is $-\frac{\sqrt{7}}{4}$  ⇒ B

Step-by-step explanation:

Let us solve the question using one of the identities of trigonometry

∵ sin²Ф + cos²Ф = 1

∵ sinФ = $\frac{3}{4}$

→ Substitute it in the rule above to find cos Ф

∴ ($\frac{3}{4}$)² + cosФ² = 1

∴ $\frac{9}{16}$ + cosФ² = 1

→ Subtract $\frac{9}{16}$  from both sides

∴ cos²Ф = $\frac{7}{16}$

→ Take √ for both sides

∴ cosФ = ± $\frac{\sqrt{7}}{4}$

∵ Angle Ф lies on the second quadrant

∴ cosФ is a negative value

∴ cosФ = $-\frac{\sqrt{7}}{4}$  

∴ cosФ is $-\frac{\sqrt{7}}{4}$