Which characteristics of a graph tell you that it represents a proportional relationship? I
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Question:
If cos(θ) =-8/17 and sin(θ) is negative, then sin(θ) = ___ and tan(θ) =___.
Answer:
Step-by-step explanation:
Given
cos(θ) =-8/17
Required
sin(θ) = __
tan(θ) =__
The first step is to determine the length of the third side
Given that
Where Adj and Hyp represent Adjacent and Hypotenuse
By comparison
Using Pythagoras
By Substitution
Subtract 64 from both sides
Take square roots of both sides
The question says that sin(θ) is negative; This implies that θ is in the third quadrant and as such
From trigonometry
Also from trigonometry
The 85th percentile is the cutoff time 
such that
In other words, the 85th percentile refers to the time needed to belong to the top 15% of the distribution; more generally, the
percentile is the top 
of the distribution.
Anyway, to find this value of, transform 
to a random variable 
with the standard normal distribution using
where
is the mean of and 
is the standard deviation of .
Here
is used to denote the z-score corresponding to the cutoff time . Referring to a z-score table, you find that this occurs for 
. So,
In other words, the 85th percentile refers to the time needed to belong to the top 15% of the distribution; more generally, the
Anyway, to find this value of
where
Here