Mathematics: If cos Θ = square root 2 over 2 and 3 pi over 2 Θ 2π, what are the values of sin Θ and tan Θ? sin Θ = square root 2 over 2; tan Θ = −1 sin Θ = negative square root 2 over 2; tan Θ = 1 sin Θ = square root 2 over 2; tan Θ = negative square root 2 sin Θ = negative square root 2 over 2; tan Θ = −1

If cos Θ = square root 2 over 2 and 3 pi over 2

Ответ:

ranchgirljls

21.01.2022

Mathematics

$\huge\boxed{\sin\theta=-\dfrac{\sqrt2}{2};\ \tan\theta=-1}$

Step-by-step explanation:

We have:

$\\cos\theta=\dfrac{\sqrt2}{2},\ \dfrac{3\pi}{2}$

For sine use:

$\sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x$

Substitute:

$\sin^2\theta=1-\left(\dfrac{\sqrt2}{2}\right)^2\\\\\sin^2\theta=1-\dfrac{(\sqrt2)^2}{2^2}\\\\\sin^2\theta=1-\dfrac{2}{4}\\\\\sin^2\theta=\dfrac{4}{4}-\dfrac{2}{4}\\\\\sin^2\theta=\dfrac{4-2}{4}\\\\\sin^2\theta=\dfrac{2}{4}\to\sin\theta=\pm\sqrt{\dfrac{2}{4}}\\\\\sin\theta=\pm\dfrac{\sqrt2}{\sqrt4}\\\\\sin\theta=\pm\dfrac{\sqrt2}{2}$

θ in IV quadrant, therefore sine is negative.

$\sin\theta=-\dfrac{\sqrt2}{2}$

For tangent use:

$\tan x=\dfrac{\sin x}{\cos x}$

Substitute:

$\tan\theta=\dfrac{-\frac{\sqrt2}{2}}{\frac{\sqrt2}{2}}=-\dfrac{\sqrt2}{2}\cdot\dfrac{2}{\sqrt2}=-1$

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Ответ:

AdoNice

09.06.2023

Mathematics

Qualitative/nominal

Gender is expressed as qualitative and nominal. Qualitative because it doesn't have a number, so it's not quantitative. It also nominal because gender is considered as having the same level. Another example of nominal is blood group or religion.
If it has an order of level(example: severity mild to severe), it will be ordinal.

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