If 5 sin-12 cos-0- find the values of sec -

The correct option is C 13/5Given, 5 sin θ 12 cos θ = 0 5 sin θ = 12 cos θ sin θ/cos θ = 12/5 = tan θ We know that, sec^2 θ = 1 + tan^2 θ nbsp; nb ...

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Standard X

Mathematics

Trigonometric Ratio(sec,cosec,cot)

If 5 sinθ-12 ...

Question

If $5 s i n θ - 12 c o s θ = 0$ , find the values of $s e c θ$ .

\frac{12}{5}

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\frac{12}{13}

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\frac{13}{5}

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\frac{5}{13}

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Solution

The correct option is C $\frac{13}{5}$
Given,
$5 s i n θ - 12 c o s θ = 0$
$5 s i n θ = 12 c o s θ$
$\frac{s i n θ}{c o s θ} = \frac{12}{5} = t a n θ$

We know that,
$s e c^{2} θ = 1 + t a n^{2} θ$
$= 1 + (\frac{12}{5})^{2}$
$= 1 + (\frac{144}{25})$
$= \frac{169}{25}$
$s e c θ = \sqrt{(\frac{169}{25})}$
$= \frac{13}{5}$

Hence, $s e c θ = \frac{13}{5}$

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Similar questions

Q. Find the maximum and minimum values of each of the following trigonometrical expressions:

(i) 12 sin θ − 5 cos θ
(ii) 12 cos θ + 5 sin θ + 4
(iii)

5 \cos θ + 3 \sin (\frac{π}{6} - θ) + 4

(iv) sin θ − cos θ + 1

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If 5 sin θ−12 cos θ=0, find the values of sec θ.

The correct option is C 135Given, 5 sin θ−12 cos θ=0 5 sin θ=12 cos θ sin θcos θ=125=tan θ We know that, sec2θ=1+tan2 θ =1+(125)2 =1+(14425) =16925 sec θ=√(16925) =135 Hence, sec θ=135

If $5 s i n θ - 12 c o s θ = 0$ , find the values of $s e c θ$ .