Mathematics: Find the exact values of a) sec of theta b)tan of theta if cos of theta= -4/5 and sin 0

Find the exact values of a) sec of theta b)tan of

Ответ:

gudtavosanchez19

17.01.2022

Mathematics

Using trigonometric ratio:

$\sec \theta = \frac{1}{\cos \theta}$

$\tan \theta = \frac{\sin \theta}{\cos \theta}$

From the given statement:

$\cos \theta = -\frac{4}{5}$ and sin < 0

⇒ $\theta$ lies in the 3rd quadrant.

then;

$\sec \theta = \frac{1}{-\frac{4}{5}} = -\frac{5}{4}$

Using trigonometry identities:

$\sin \theta = \pm \sqrt{1-\cos^2 \theta}$

Substitute the given values we have;

$\sin \theta = \pm\sqrt{1-(\frac{-4}{5})^2 } =\pm\sqrt{1-\frac{16}{25}} =\pm\sqrt{\frac{25-16}{25}} =\pm \sqrt{\frac{9}{25} } = \pm\frac{3}{5}$

Since, sin < 0

⇒ $\sin \theta = -\frac{3}{5}$

now, find $\tan \theta$ :

$\tan \theta = \frac{\sin \theta}{\cos \theta}$

Substitute the given values we have;

$\tan \theta = \frac{-\frac{3}{5} }{-\frac{4}{5} } = \frac{3}{5}\times \frac{5}{4} = \frac{3}{4}$

Therefore, the exact value of:

(a)

$\sec \theta =-\frac{5}{4}$

(b)

$\tan \theta= \frac{3}{4}$

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Ответ:

lisa123465

02.05.2023

Mathematics

Part A: Yes, the first data represents a function. By the book definition, a function is a relation in which no value of x will have two different values of y. This means that we can have two similar values of y with two different values of x but not the other way around.
None of the numbers for the table of x repeat, therefore we can safely say that the relation is a function.

Part B: For this part, all we have to do is to plug in x = 4 in the 2nd relation,

f(x) = 2(4) – 8 = 0

In the table, when x = 4, y = 9. Therefore the function described in the table has greater value.

Part C: Again all we have to do is to plug in x = 34 in the 2nd relation,
f(x) = 2(34) – 8

f(x) = 60

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Find the exact values of a) sec of theta b)tan of theta if cos of theta= -4/5 and sin< 0

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