provide me all the trigonometric identities
Answers
Answer:
Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent
For a given angle θ each ratio stays the same
no matter how big or small the triangle is
When we divide Sine by Cosine we get:
sin(θ)cos(θ) = Opposite/HypotenuseAdjacent/Hypotenuse = OppositeAdjacent = tan(θ)
So we can say:
tan(θ) = sin(θ)cos(θ)
That is our first Trigonometric Identity.
Cosecant, Secant and Cotangent
We can also divide "the other way around" (such as Adjacent/Opposite instead of Opposite/Adjacent):
triangle showing Opposite, Adjacent and Hypotenuse
Cosecant Function:
csc(θ) = Hypotenuse / Opposite
Secant Function:
sec(θ) = Hypotenuse / Adjacent
Cotangent Function:
cot(θ) = Adjacent / Opposite
Example: when Opposite = 2 and Hypotenuse = 4 then
sin(θ) = 2/4, and csc(θ) = 4/2
Because of all that we can say:
sin(θ) = 1/csc(θ)
cos(θ) = 1/sec(θ)
tan(θ) = 1/cot(θ)
And the other way around:
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
And we also have:
cot(θ) = cos(θ)/sin(θ)
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Answer:
Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent
For a given angle θ each ratio stays the same
no matter how big or small the triangle is
When we divide Sine by Cosine we get:
sin(θ)cos(θ) = Opposite/HypotenuseAdjacent/Hypotenuse = OppositeAdjacent = tan(θ)
So we can say:
tan(θ) = sin(θ)cos(θ)
That is our first Trigonometric Identity.
Cosecant, Secant and Cotangent
We can also divide "the other way around" (such as Adjacent/Opposite instead of Opposite/Adjacent):
triangle showing Opposite, Adjacent and Hypotenuse
Cosecant Function:
csc(θ) = Hypotenuse / Opposite
Secant Function:
sec(θ) = Hypotenuse / Adjacent
Cotangent Function:
cot(θ) = Adjacent / Opposite
Example: when Opposite = 2 and Hypotenuse = 4 then
sin(θ) = 2/4, and csc(θ) = 4/2
Because of all that we can say:
sin(θ) = 1/csc(θ)
cos(θ) = 1/sec(θ)
tan(θ) = 1/cot(θ)
And the other way around:
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
And we also have:
cot(θ) = cos(θ)/sin(θ)
السوال هو ما معنى الرخصة الشرعية ؟ وما الحكمة م
500thx+follow=inbox ✌