Answer:
The value of cosФ = -√5/3
Step-by-step explanation:
∵ sinФ = 2/3
∵ tanФ is less than 0
* Lets think about that:
the value of sin is positive and the value of tan is negative
according to ASTC rule:
- All are positive in the first quadrant
- sin only positive in the second quadrant
- tan only positive in the third quadrant
- cos only positive in the fourth quadrant
∴ Angle Ф lies on the second quadrant
∴ The value of cosФ is less than 0
∵ sin²Ф + cos²Ф = 1
∵ sinФ = 2/3
∴ (2/3)² + cos²Ф = 1
∴ cos²Ф = 1 - 4/9 = 5/9
∴ cosФ = ± √5/3
∵ Angle Ф lies on second quadrant
∴ cosФ = -√5/3
