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Write the expression in terms of the appropriate cofunction. cot(25°)
A
tan(65°)
B
tan(25°)
C
cot(65°)
D
cot(25°)
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1
Understand the concept of cofunctions: Cofunctions are pairs of trigonometric functions that are complementary, meaning they add up to 90 degrees. For example, sine and cosine are cofunctions, as are tangent and cotangent.
Identify the cofunction relationship: The cotangent function, \( \cot(\theta) \), is the cofunction of the tangent function, \( \tan(90° - \theta) \).
Apply the cofunction identity: Since \( \cot(\theta) = \tan(90° - \theta) \), we can rewrite \( \cot(25°) \) in terms of its cofunction.
Calculate the complementary angle: The complementary angle to 25° is 65°, because 90° - 25° = 65°.
Rewrite the expression: Using the cofunction identity, \( \cot(25°) \) can be expressed as \( \tan(65°) \).