Find sin 0 and tan 0 when cos 0 = 2/5

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30-10-2022
Mathematics

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Find sin 0 and tan 0 when cos 0 = 2/5

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CosimoU29347 CosimoU29347 · Answer 1 · 2022-10-30T08:49:01+01:00

ANSWER:

[tex]\begin{gathered} \sin \theta=\frac{\sqrt[]{21}}{5} \\ \tan \theta=\frac{\sqrt[]{21}}{2} \end{gathered}[/tex]

STEP-BY-STEP EXPLANATION:

We have the following:

[tex]\cos \theta=\frac{2}{5}[/tex]

Which means that the adjacent leg of the triangle is equal to 2 and the hypotenuse is equal to 5.

We can calculate the value of the opposite leg by means of the Pythagorean theorem as follows

[tex]\begin{gathered} h^2=a^2+b^2 \\ 5^2=2^2+b^2 \\ \text{solving for b:} \\ b^2=25-4 \\ b=\sqrt[]{21} \end{gathered}[/tex]

Knowing the value of the opposite leg we can calculate the value of the other trigonometric ratios:

[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{\sqrt[]{21}}{5} \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{\sqrt[]{21}}{2} \end{gathered}[/tex]