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nevsk [136]
2 years ago
14

Jacob’s parents have allowed him to get a cell phone but he must pay his own cell phone bill. He pays a flat rate of $35 and $0.

50 for every minute he talks on the phone. If y represents the total cost of the bill and x represents minutes talking on the phone, which equation best fits the situation?
Mathematics
1 answer:
Annette [7]2 years ago
6 0

Answer:

35 plus x.50=y

Step-by-step explanation:

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Find the value of tan( π + θ) if θ terminates in Quadrant III and sinθ = -5/13
Vladimir79 [104]

ANSWER

\tan(\pi +  \theta)= \frac{5}{12}

EXPLANATION

We first obtain

\cos( \theta)

using the Pythagorean Identity.

\cos ^{2} ( \theta)  + \sin ^{2} ( \theta)  = 1

\implies \: \cos ^{2} ( \theta)  + (  - \frac{5}{13} )^{2} = 1

\implies \: \cos ^{2} ( \theta)  + \frac{25}{169}= 1

\implies \: \cos ^{2} ( \theta) = 1 - \frac{25}{169}

\implies \: \cos ^{2} ( \theta) =  \frac{144}{169}

\implies \: \cos ( \theta) =  \pm \:  \sqrt{\frac{144}{169} }

\implies \: \cos ( \theta) =  \pm \:  \frac{12}{13}

In the third quadrant, the cosine ratio is negative.

\implies \: \cos ( \theta) =   -  \:  \frac{12}{13}

The tangent function has a period of π and \pi +  \theta is in the third quadrant.

This implies that:

\tan(\pi +  \theta)= \tan(  \theta)

\tan(\pi +  \theta)= \frac{ \sin(  \theta) }{ \cos(  \theta) }

\tan(\pi +  \theta)=  \frac{  - \frac{ 5}{13} }{  - \frac{12}{13} }

This gives us:

\tan(\pi +  \theta)= \frac{5}{12}

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