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

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn