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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find sin(α) and cos(β), tan(α) and cot(β), and sec(α) and csc(β). The hypotenuse is 7 and the side is 4.
Solution:
The problem statement can be represented as:
Since it is a right angled triangle we can write
AC² = AB² + BC²
(7)² = (AB)² + (4)²
(AB)² = 49 - 16 = 33
AB = √33
sin(α) = AB/AC = √33/7
cos(β) = AB/AC = √33/7
tan(α) = AB/BC = √33/4
cot(β) = 1/tan(β)
tan(β) = BC/AB = 4/√33
therefore
cot(β) = √33/4
sec(α) = 1/cos(α)
cos(α) = 4/7
Therefore
sec(α) = 1/(4/7) = 7/4
csc(β) = 1/sin(β)
sin(β) = 4/7
Therefore
csc(β) = 1/sin(β) = 1/(4/7)
csc(β) = 7/4
Find sin(α) and cos(β), tan(α) and cot(β), and sec(α) and csc(β). The hypotenuse is 7 and the side is 4
Summary:
sin(α) = √33/7 and cos(β) = √33/7; tan(α) = √33/4 and cot(β)= √33/4 , and sec(α) = 7/4 and csc(β) = 7/4
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