Problem:
Find the remaining trigonometric ratios of the acute angle ϴ, given that sin ϴ= 5/7
Solution:
Use pythagorean theorem
c² = a² + b²
7² = 5² + b²
49 = 25 + b²
b² = 49 - 25
b² = 24
b = √24
b = 2√6
Sine ϴ = opposite side / hypotenuse
Cosine ϴ = adjacent side / hypotenuse
Tangent ϴ = Opposite side / adjacent side
Cosecant ϴ = hypotenuse / opposite side
Secant ϴ = hypotenuse / adjacent side
Cotangent ϴ = adjacent side / opposite side
sin ϴ = 5/7
cos ϴ = (2√6)/7
tan ϴ = 5/(2√6)
csc ϴ = 7/5
sec ϴ = 7/(2√6)
cot ϴ = (2√6)/5
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