Mathematics: Sandra knows the pythagorean identity sin 2 ⁡ θ + cos 2 ⁡ θ = 1 . if she is told that 0 ≤ θ ≤ π 2 and cos ⁡ θ = 5 12, what will she get when she correctly calculates tan ⁡ θ ?

Sandra knows the pythagorean identity sin 2 ⁡ θ

Ответ:

jazzyjaz2003

15.01.2022

$\text{tan}(\theta)=\frac{\sqrt{119}}{5}$

Step-by-step explanation:

We have been given that Sandra knows the Pythagorean identity $\text{sin}^2(\theta)+\text{cos}^2(\theta)=1$ . She is told that $0\leq \theta\leq \frac{\pi}{2}$ and $\text{cos}(\theta)=\frac{5}{12}$ .

First of all, we will find value of sine theta using the given identity.

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

$\text{sin}^2(\theta)+(\frac{5}{12})^2=1$

$\text{sin}^2(\theta)+\frac{25}{144}=1$

$\text{sin}^2(\theta)+\frac{25}{144}-\frac{25}{144}=1-\frac{25}{144}$

$\text{sin}^2(\theta)=\frac{144-25}{144}$

$\text{sin}^2(\theta)=\frac{119}{144}$

$\text{sin}(\theta)=\sqrt{\frac{119}{144}}$

$\text{sin}(\theta)=\frac{\sqrt{119}}{12}$

$\text{tan}(\theta)=\frac{\text{sin}(\theta)}{\text{cos}(\theta)}$

$\text{tan}(\theta)=\frac{\frac{\sqrt{119}}{12}}{\frac{5}{12}}$

$\text{tan}(\theta)=\frac{\sqrt{119}*12}{5*12}=\frac{\sqrt{119}}{5}$

Therefore, $\text{tan}(\theta)=\frac{\sqrt{119}}{5}$ .

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Ответ:

bks53

28.10.2020

Mathematics

3/4

Step-by-step explanation:

We can find the slope given two points by using

m = (y2-y1)/(x2-x1) where one point is (x1,y1) and the other is (x2,y2)

We have the points (4,7) and(8,10)

= (10-7)/(8-4)

= 3/4

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Sandra knows the pythagorean identity sin 2 ⁡ θ + cos 2 ⁡ θ = 1 . if she is told that 0 ≤ θ ≤ π 2 and cos ⁡ θ = 5 12, what will she get when she correctly calculates tan ⁡ θ ?

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