If sign Tera angle equal 2/3 and tangent test angle is less than zero what is the value of cosine teta angle

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