The coattribute identities show the connection in between sine, cosine, tangent, cotangent, secant and also cosecant. The worth of a trigonometric attribute of an angle equates to the worth of the cofunction of the complement. Respeak to from geometry that a enhance is defined as 2 angles whose amount is 90°.For example: Given that the
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the enhance of
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Radians

Sine and also cosine are cofeatures and also complements

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*

Tangent and cotangent are coattributes and also complements

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*

Secant and also cosecant are cofeatures and complements

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Degree

Sine and also cosine are cofeatures and also complements

sin(90° - x) = cos x

cos(90° - x) = sin x

Tangent and also cotangent are cofeatures and also complements

tan(90° - x) = cot x

cot(90° - x) = tan x

Secant and cosecant are cofeatures and also complements

sec(90° - x) = csc x

csc(90° - x) = sec x

Degree Example:

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sin A = cos B = A =
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B =
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cos(90° - A) = sin AUsing substitution:cos(90° - 67.4°) = sin 67.5°cos(22.6°) = sin(67.5)°
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As such, the worth of cosine B is equal to sine A which is the cofunction and also match of B. The process remains the very same whether you are in level mode or radian mode.Let"s view just how this deserve to be used.
Use the coattribute identities to evaluate the expression without a calculator! sin2 (23°) + sin2 (67°)Step 1: Note that 23° + 67° = 90° (complementary)

Tip 2: usage the coattribute identity and let x = 23°sin(90° - x) = cos x

therefore sin(67°) = cos(23°)

Tip 3: use substitution sin2(23°) + cos2(23°)

Tip 4: use the Pythagorean identity sin2θ + cos2θ = 1sin2(23°) + cos2(23°) = 1


Thus, sin2(23°) + sin2(67°) = sin2(23°) + cos2(23°) = 1


Related Links:Math Trigonomeattempt Sum and Difference of Angles IdentitiesTrigonometric Identities - Reciprocal Identities

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