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Frequently Asked Questions (FAQ)
What are trigonometric identities?
Trigonometric identities are mathematical equations that involve trigonometric functions such as sine, cosine, and tangent, and are true for all values of the variables in the equation.
What are the types of trigonometric identities?
The most common types of trigonometric identities include the Pythagorean Identities, Reciprocal Identities, Quotient Identities, Co-function Identities, Double Angle identities, and Half Angle identities.
What are Pythagorean identities?
The Pythagorean identities are a set of trigonometric identities that are based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. The most common Pythagorean identities are:
sin²x + cos²x = 1
1 + tan²x = sec²x
What are reciprocal Identities?
Reciprocal identities are a set of trigonometric identities that relate the reciprocal of one trigonometric function to the other. The reciprocal identities are:
cscx = 1/sinx
secx = 1/cosx
cotx = 1/tanx
What are Quotient Identities?
Quotient identities are a set of trigonometric identities that relate the quotient of two trigonometric functions to another function. The quotient identities are:
tanx = sinx/cosx
cotx = cosx/sinx
secx/cscx = cosx/sinx
What are Co-function Identities?
Co-function identities are a set of trigonometric identities that relate the trigonometric functions of complementary angles. Complementary angles are two angles whose sum is 90 degrees. The co-function identities are:
sin(90-x) = cosx
cos(90-x) = sinx
tan(90-x) = cotx
What are Double Angle Identities?
Double angle identities are a set of trigonometric identities that express the value of a trigonometric function of twice an angle in terms of the value of the function of the angle. The most common double angle identities are:
sin(2x) = 2sinxcosx
cos(2x) = cos²x - sin²x
tan(2x) = (2tanx)/(1-tan²x)
What are Half Angle identities?
Half angle identities are a set of trigonometric identities that express the value of a trigonometric function of half an angle in terms of the value of the function of the angle. The most common half angle identities are:
sin(x/2) = ±√{[1-cosx]/2}
cos(x/2) = ±√{[1+cosx]/2}
tan(x/2) = ±√{[1-cosx]/[1+cosx]}