Answer:
cosФ is [tex]-\frac{\sqrt{7}}{4}[/tex] ⇒ B
Step-by-step explanation:
Let us solve the question using one of the identities of trigonometry
∵ sin²Ф + cos²Ф = 1
∵ sinФ = [tex]\frac{3}{4}[/tex]
→ Substitute it in the rule above to find cos Ф
∴ ([tex]\frac{3}{4}[/tex])² + cosФ² = 1
∴ [tex]\frac{9}{16}[/tex] + cosФ² = 1
→ Subtract [tex]\frac{9}{16}[/tex] from both sides
∴ cos²Ф = [tex]\frac{7}{16}[/tex]
→ Take √ for both sides
∴ cosФ = ± [tex]\frac{\sqrt{7}}{4}[/tex]
∵ Angle Ф lies on the second quadrant
∴ cosФ is a negative value
∴ cosФ = [tex]-\frac{\sqrt{7}}{4}[/tex]
∴ cosФ is [tex]-\frac{\sqrt{7}}{4}[/tex]
