Answer:
The value of sin Ф is [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
In quadrant II, the value of
Let us solve the question
∵ sin²Ф + cos²Ф = 1
∵ cos Ф = [tex]\frac{-12}{13}[/tex]
→ Substitute it in the identity above
∴ sin²Ф + ([tex]\frac{-12}{13}[/tex])² = 1
∴ sin²Ф + [tex]\frac{144}{169}[/tex] = 1
→ Subtract [tex]\frac{144}{169}[/tex] from both sides
∵ sin²Ф + [tex]\frac{144}{169}[/tex] - [tex]\frac{144}{169}[/tex] = 1 - [tex]\frac{144}{169}[/tex]
∴ sin²Ф = [tex]\frac{25}{169}[/tex]
→ Take the square root of both sides
∵ √(sin²Ф)= ± [tex]\sqrt{\frac{25}{169}}[/tex]
∴ sin Ф = ± [tex]\frac{5}{13}[/tex]
∵ Ф is in quadrant II
∴ sin Ф is a positive value
∴ sin Ф = [tex]\frac{5}{13}[/tex]
∴ The value of sin Ф is [tex]\frac{5}{13}[/tex]
