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# 7) Find the exact value of sec θ given tan θ = 3 and cos θ > 0. Show all Work

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Can anybody help me with this one math problem I have? I still need this question answered here. Thank You!

Feb 3, 2020

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An Identity:

$$sec^2(\theta)= 1+tan^2(\theta)$$

"Given $$tan(\theta)=3$$

I think that's all we need?

then

$$tan^2(\theta)=3^2=9$$

$$sec^2(\theta)=1+9=10$$

$$sec(\theta)=\sqrt{10}=3.16227766..approx.=3.16$$

We didn't take the negative square root since:

$$cos(\theta)>0$$ and $$sec(\theta)=\frac{1}{cos(\theta)}$$

Thus $$sec(\theta)$$ must be positive.

Feb 3, 2020