Find the exact values of the five remaining trigonometric functions of θ. please help with math?
:-
r² = 6² + 7²
r² = 36 + 49
r² = 85
r = √85
tan ∅ = - 7/6________cot ∅ = - 6/7
cos ∅ = 6/√85_____sec ∅ = √85/6
sin ∅ = - 7/√85_____csc ∅ = - √85/7
cotθ => 1/tanθ so,
tanθ = -7/6
Terminal side length l is 7² + 6² = l²
i.e. l² = 85
=> l = √85
so, sinθ = -7/√85 and cosθ = 6/√85
Now, secθ => 1/cosθ = √85/6
and cosecθ => 1/sinθ = -√85/7
Note: only cosθ and secθ are positive in QIV
:)>
if cot Θ = - 6 / 7 the the reference triangle for Θ is { 6 , - 7 , √85 } ===> sin Θ = - 7 / √85 , etc..
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Verified answer
:-
r² = 6² + 7²
r² = 36 + 49
r² = 85
r = √85
tan ∅ = - 7/6________cot ∅ = - 6/7
cos ∅ = 6/√85_____sec ∅ = √85/6
sin ∅ = - 7/√85_____csc ∅ = - √85/7
cotθ => 1/tanθ so,
tanθ = -7/6
Terminal side length l is 7² + 6² = l²
i.e. l² = 85
=> l = √85
so, sinθ = -7/√85 and cosθ = 6/√85
Now, secθ => 1/cosθ = √85/6
and cosecθ => 1/sinθ = -√85/7
Note: only cosθ and secθ are positive in QIV
:)>
if cot Θ = - 6 / 7 the the reference triangle for Θ is { 6 , - 7 , √85 } ===> sin Θ = - 7 / √85 , etc..