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Vilka [71]
3 years ago
14

The angle θ is in the first quadrant of the unit circle and tan(θ)=

="TexFormula1" title="\frac{8}{15}" alt="\frac{8}{15}" align="absmiddle" class="latex-formula"> .Since tan(θ)=\frac{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).
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
5 0

Answer:

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

Step-by-step explanation:

Given:

Angle lies in first quadrant.

\tan\theta=\frac{8}{15}

Since, \tan\theta=\frac{\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=\frac{8}{15}

So,

\theta=\tan^{-1}(\frac{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

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