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Answer:
Answer:
Trigonometric Functions of Acute Angles
sin X = opp / hyp = a / c , csc X = hyp / opp = c / a
tan X = opp / adj = a / b , cot X = adj / opp = b / a
cos X = adj / hyp = b / c , sec X = hyp / adj = c / b ,
acute angle trigonometric functions.
Trigonometric Functions of Arbitrary Angles
sin X = b / r , csc X = r / b
tan X = b / a , cot X = a / b
cos X = a / r , sec X = r / a
acute angle trigonometric functions.
Special Triangles
Special triangles may be used to find trigonometric functions of special angles: 30, 45 and 60 degress.
special triangles.
Sine and Cosine Laws in Triangles
In any triangle we have:
1 - The sine law
sin A / a = sin B / b = sin C / c
2 - The cosine laws
a
2 = b 2 + c 2 - 2 b c cos A
b 2 = a 2 + c 2 - 2 a c cos B
c 2 = a 2 + b 2 - 2 a b cos C
triangles.
Relations Between Trigonometric Functions
cscX = 1 / sinX
sinX = 1 / cscX
secX = 1 / cosX
cosX = 1 / secX
tanX = 1 / cotX
cotX = 1 / tanX
tanX = sinX / cosX
cotX = cosX / sinX
Pythagorean Identities
sin 2X + cos 2X = 1
1 + tan 2X = sec 2X
1 + cot 2X = csc 2X
Negative Angle Identities
sin(-X) = - sinX , odd function
csc(-X) = - cscX , odd function
cos(-X) = cosX , even function
sec(-X) = secX , even function
tan(-X) = - tanX , odd function
cot(-X) = - cotX , odd function
Cofunctions Identities
sin(π/2 - X) = cosX
cos(π/2 - X) = sinX
tan(π/2 - X) = cotX
cot(π/2 - X) = tanX
sec(π/2 - X) = cscX
csc(π/2 - X) = secX
Step-by-step explanation: