Question

If sin tetha=root3/2, what is cos tetha?​

Answer 1

The value of cos Ф is ±
`(1)/(2)`

Explanation:

There are important rules for sin Ф and cos Ф

• sin²Ф + cos²Ф = 1

• sin²Ф = 1 - cos²Ф

• cos²Ф = 1 - sin²Ф

∵ sin Ф =
`(√(3))/(2)`

∴ sin²Ф =
`((√(3))/(2))^(2)`

∴ sin²Ф =
`(3)/(4)`

→ By using the third rule above

∵ cos²Ф = 1 - sin²Ф

∴ cos²Ф = 1 -
`(3)/(4)`

∴ cos²Ф =
`(1)/(4)`

→ Take square root for both sides

∴ cos Ф = ±
`(1)/(2)`

∴ The value of cos Ф is ±
`(1)/(2)`