Question

Consider angle θ in Quadrant lI, where cosθ = - 12/13. What is the value of sinθ?​

Answer 1

Answer:

The value of sin Ф is $\frac{5}{13}$

Step-by-step explanation:

In quadrant II, the value of

• sin Ф is positive

• cos Ф is negative

• tan Ф is negative

Let us solve the question

∵ sin²Ф + cos²Ф = 1

∵ cos Ф = $\frac{-12}{13}$

→ Substitute it in the identity above

∴ sin²Ф + ($\frac{-12}{13}$)² = 1

∴ sin²Ф + $\frac{144}{169}$ = 1

→ Subtract $\frac{144}{169}$ from both sides

∵ sin²Ф + $\frac{144}{169}$  - $\frac{144}{169}$  = 1 - $\frac{144}{169}$

∴ sin²Ф = $\frac{25}{169}$

→ Take the square root of both sides

∵ √(sin²Ф)= ± $\sqrt{\frac{25}{169}}$

∴ sin Ф = ± $\frac{5}{13}$

∵ Ф is in quadrant II

∴ sin Ф is a positive value

∴ sin Ф = $\frac{5}{13}$

∴ The value of sin Ф is $\frac{5}{13}$