Question

1.An acute angle _ is in a right triangle with cos _ =(5)/(6) . What is the value of sec _?

2.An acute angle _ is in a right triangle with sin _ = (5)/(6) . What is the value of cot _?"

Answer 1

1)
Cosine = base / hypotenuse
Secant = hypotenuse / base = 1/Cosine
Sec = 1/(5/6) = 6/5
2)
Sine = perpendicular / hypotenuse = 5/6
hypotenuse² = base² + perpendicular²
base = √(6² - 5²)
base = √11
Cotangent = base / perpendicular
= √11/5