4 years ago

Need some help with this!

Mathematics

1 answer:

Morgarella [4.7K]4 years ago

8 0

Answer:

substitution

reflexive

Step-by-step explanation:

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What is 2x+3y=17 if y=-3

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Step-by-step explanation:

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3 years ago

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If t a n squared θ = 3 /8 , what is the value of s e c θ

TEA [102]

We can use 3 facts:

$\tan{\theta}=\frac{y}{x}$

$\sec{\theta}=\frac{r}{x}$

$x^2+y^2=r^2$

So, to find our x and our y we can do:

$\tan^2{\theta}=\frac{3}{8} \implies \\ \tan{\theta}=\pm{\sqrt{\frac{3}{8}}=\pm\frac{\sqrt{3}}{\sqrt{8}}$ So, now that we know our x and our y we can find our r.

$(\sqrt{3})^2+(\sqrt{8})^2=11 \implies r=\sqrt{11}$

You'll notice, though, that there were two solutions for $\tan{\theta}$ , which means we have a positive and a negative for our x. So:

$\sec{\theta}=\frac{\sqrt{11}}{\sqrt{8}} \\ \sec{\theta}=-\frac{\sqrt{11}}{\sqrt{8}}}\\ \text{Rationalizing both of them:}\\ \sec{\theta}=\frac{\sqrt{88}}{8} \\ \sec{\theta}=-\frac{\sqrt{88}}{8}$