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1 vote
The angle θ is in the first quadrant of the unit circle and tan(θ)=
(8)/(15) .Since tan(θ)=
(sin(θ))/(cos(θ)) , does this mean that sin(θ)=8 and cos(θ)=15? If not, clearly explain and give the exact values of sin(θ) and cos(θ).

User Jaxb
by
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1 Answer

4 votes

Answer:


\sin(\theta)=0.47 and
\cos(\theta)=0.88.

Explanation:

Given:

Angle lies in first quadrant.


\tan\theta=(8)/(15)

Since,
\tan\theta=(\cos(\theta)/(\sin(\theta)) this does not mean that
\sin(\theta)=8 and
\cos(\theta)=15, because it is the ratio of the
\sin(\theta) and
\cos(\theta) which is not necessarily the exact values of them. And also
\sin(\theta) and
\cos(\theta) values lie between
-1 \ to\ 1 and so it cannot be
=8\ or\ 15.

In order to find the exact values, we need to find the exact angle.


\tan\theta=(8)/(15)

So,


\theta=\tan^(-1)((8)/(15))


\theta= 28.07\° As the angle lies in 1st quadrant.

Using the angle
\theta we can find the exact values for
\sin(\theta) and
\cos(\theta).


sin(28.07\°)=0.47


cos(28.07\°)=0.88

User Kenniesha
by
7.8k points

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