MATH SOLVE

3 months ago

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

Accepted Solution

A:

Answer:The value of cosФ = -√5/3Step-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