Find tan θ if sec θ = square root of thirty seven divided by six and sin θ < 0.
Asked by maham237 @ in Mathematics viewed by 309 People
Answered by maham237 @
We know that
sec²θ=tan²θ+1-------> tan²θ=> sec²θ-1
sec θ = (√37)/6
tan²θ=> [(√37)/6]²-1--------> (37/36)-1-------> 1/36
tanθ=√(1/36)--------> 1/6
remember that
sec θ = 1/ cos θ
the cos θ is > 0
and
the sin θ < 0
so the angle θ belong to the fourth quadrant-------> tan θ is negative
therefore
the answer is
tan θ=-1/6
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