How do you find the exact value of cot(arcsin(-12/13))

nabakhi72

nabakhi72

Answered question

2022-08-14

How do you find the exact value of cot ( arcsin ( 12 13 ) )?

Answer & Explanation

gorilomgl

gorilomgl

Beginner2022-08-15Added 9 answers

Remember that the arcsin function is defined as having a range ( π 2 , + π 2 ]
The arcsin ( 12 13 ) can be represented by a triangle in the standard position with opposite side (i.e. y coordinate): (-12) and hypotenuse (13)
Based on the Pythagorean Theorem, this triangle would have an adjacent side with the length 13 2 ( 12 ) 2 = 5
Since cot = a d j a c e n t o p p o s i t e
cot ( arcsin ( 12 13 ) ) = 5 12 = 5 12

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