Question

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

Answer 1

The value of sin Ф is
`(5)/(13)`

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 =
`(-12)/(13)`

→ Substitute it in the identity above

∴ sin²Ф + (
`(-12)/(13)`)² = 1

∴ sin²Ф +
`(144)/(169)` = 1

→ Subtract
`(144)/(169)` from both sides

∵ sin²Ф +
`(144)/(169)` -
`(144)/(169)` = 1 -
`(144)/(169)`

∴ sin²Ф =
`(25)/(169)`

→ Take the square root of both sides

∵ √(sin²Ф)= ±
`\sqrt{(25)/(169)}`

∴ sin Ф = ±
`(5)/(13)`

∵ Ф is in quadrant II

∴ sin Ф is a positive value

∴ sin Ф =
`(5)/(13)`

∴ The value of sin Ф is
`(5)/(13)`