Suppose that β is an acute angle and sec β = 11 . 3. How to do the following?

Question

Suppose that β is an acute angle and sec β = 11 . 3. How to do the following?

(a) Find the exact value of: (i) cosec β, (ii) cot β.

(b) Show that $c o$ $co$ ${sec}^{2}$ $sec^2$ β − ${cot}^{2}$ $cot^2$ β = 1.

1 Answer

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Answer 1 · 2018-05-19T22:28:38

cosec b = 1.0039
cot b = 0.0888

Explanation:

$sec b = 11.3$ $sec b = 11.3$ -->
$cos b = \frac{1}{11.3} = 0.0885$ $cos b = 1/11.3 = 0.0885$ . Find sin b.
${sin}^{2} b = 1 - {cos}^{2} b = 1 - 0.0078 = 0.9921$ $sin^2b = 1 - cos^2 b = 1 - 0.0078 = 0.9921$
$sin b = 0.9960$ $sin b = 0.9960$
cosec b = $\frac{1}{sin b} = 1.0039$ $1/(sin b) = 1.0039$
$cot b = \frac{cos b}{sin b} = \frac{0.0085}{0.9960} = 0.0888$ $cot b = cos b/(sin b) = 0.0085/(0.9960) = 0.0888$

$cos e c^{2} b - {cot}^{2} b = 1.0078 - 0.0078 = 1$ $cosec^2 b - cot^2 b = 1.0078 - 0.0078 = 1$ . Proved

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Suppose that β is an acute angle and sec β = 11 . 3. How to do the following?

(a) Find the exact value of: (i) cosec β, (ii) cot β.

(b) Show that $c o$ $co$ ${sec}^{2}$ $sec^2$ β − ${cot}^{2}$ $cot^2$ β = 1.

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

Suppose that β is an acute angle and sec β = 11 . 3. How to do the following?

(a) Find the exact value of: (i) cosec β, (ii) cot β. (b) Show that cocosec2sec^2 β − cot2cot^2 β = 1.

1 Answer

Explanation:

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Impact of this question

(a) Find the exact value of: (i) cosec β, (ii) cot β.

(b) Show that $c o$ $co$ ${sec}^{2}$ $sec^2$ β − ${cot}^{2}$ $cot^2$ β = 1.