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Mathematics
Merritt
21 November, 22:09
Find the exact value of tan (cos^-1 (-5/13))
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Valentino Gamble
21 November, 23:36
0
-¹²/₅
Step-by-step explanation:
Let cos a = - ⁵/₁₃
Then tan a = sin a/cos a
= [√ (1 - cos²a) ]/cos a
= {√[1 - (-⁵/₁₃) ²]} / (-⁵/₁₃)
= - [√ (1 - ²⁵/₁₆₉) ] * ¹³/₅
= - [ (√ (¹⁴⁴/₁₆₉) ] * ¹³/₅
= - ¹²/₁₃ * ¹³/₅
= - ¹²/₅
tan (arccos (-⁵/₁₃)) = - ¹²/₅
The diagram shows the 2nd quadrant of a circle with radius 13, cos a = - ⁵/₁₃, and tan a = ¹²/₍₋₅₎ = - ¹²/₅.
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