In each of the following- one of the six stigonometric ratios is given- Find the values of the other trigonometric ratios- i sin-A-2-3 ii cos-A-4-5 iii tan- - 11 iv sin- -11-15 v tan- -5-12 vi sin- -3-2 vii cos- -7-25 viii tan- -8-15 ix cot- -12-5 x sec- -13-5 xi cosec- -10 xii cos- -12-15

(i) cos A=√(5)/3,tan A=2/√(5),sec A=3/√(5),cosec A=3/2,cot A√(5)/2 (ii) sin A=3/5,tan A=3/4,sec A=5/4,cosec A=5/3,cot A=4/3 (iii) sin θ=11/√(122),cos θ=1/√(1 ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

In each of th...

Question

In each of the following, one of the six stigonometric ratios is given. Find the values of the other trigonometric ratios.

(i) $s i n A = \frac{2}{3}$

(ii) $c o s A = \frac{4}{5}$

(iii) $t a n θ = 11$

(iv) $s i n θ = \frac{11}{15}$

(v) $t a n α = \frac{5}{12}$

(vi) $s i n θ = \frac{\sqrt{3}}{2}$

(vii) $c o s θ = \frac{7}{25}$

(viii) $t a n θ = \frac{8}{15}$

(ix) $c o t θ = \frac{12}{5}$

(x) $s e c θ = \frac{13}{5}$

(xi) $c o s e c θ = \sqrt{10}$

(xii) $c o s θ = \frac{12}{15}$

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Solution

(i) $c o s A = \frac{\sqrt{5}}{3}, t a n A = \frac{2}{\sqrt{5}}, s e c A = \frac{3}{\sqrt{5}}, c o s e c A = \frac{3}{2}, c o t A \frac{\sqrt{5}}{2}$
(ii) $s i n A = \frac{3}{5}, t a n A = \frac{3}{4}, s e c A = \frac{5}{4}, c o s e c A = \frac{5}{3}, c o t A = \frac{4}{3}$
(iii) $s i n θ = \frac{11}{\sqrt{122}}, c o s θ = \frac{1}{\sqrt{122}}, c o s e c θ = \frac{\sqrt{122}}{11}, s e c θ = \sqrt{122}, c o t θ = \frac{1}{11}$

(iv) $c o s θ = \frac{2 \sqrt{2} 6}{15}, t a n θ = \frac{11}{2 \sqrt{2} 6}, s e c A = \frac{15}{2 \sqrt{2} 6}, c o t θ = \frac{2 \sqrt{2} 6}{11}, c o s e c θ = \frac{15}{11}$
(v) $s i n α = \frac{5}{13}, c o s α = \frac{12}{13}, c o t α = \frac{12}{5}, c o s e c α = \frac{13}{5}, s e c α = \frac{13}{12}$

(vi) $c o s θ = \frac{1}{2}, t a n θ = \sqrt{3}, s e c θ = 2, c o s e c θ = \frac{2}{\sqrt{3}}, c o t θ = \frac{1}{\sqrt{3}}$
(vii) $s i n θ = \frac{24}{25}, t a n θ = \frac{24}{7}, s e c θ = \frac{25}{7}, c o s e c θ = \frac{25}{24}, c o t θ = \frac{7}{24}$
(viii) $s i n θ = \frac{8}{17}, c o s θ = \frac{15}{17}, c o t θ = \frac{15}{8}, c o s e c θ = \frac{17}{8}, s e c θ = \frac{17}{15}$
(ix) $t a n θ = \frac{5}{12}, s i n θ = \frac{5}{13}, c o s θ = \frac{12}{13}, c o s e c θ = \frac{13}{5}, s e c θ = \frac{13}{12}$
(x) $s i n θ = \frac{12}{13}, c o s θ = \frac{5}{13} . t a n θ = \frac{12}{5}, c o s e c θ = \frac{13}{12}, c o t θ = \frac{5}{12}$
(xi) $s i n θ = \frac{1}{\sqrt{10}}, c o s θ = \frac{3}{\sqrt{10}}, t a n θ = \frac{1}{3}, s e c θ = \frac{\sqrt{10}}{3}, c o t θ = 3$
(xii) $s i n θ = \frac{9}{15}, t a n θ = \frac{9}{12}, c o s e c θ = \frac{15}{9}, c o t θ = \frac{12}{9}, s e c θ = \frac{15}{12}$

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Similar questions

Q. In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

(i)

\sin A = \frac{2}{3}

(ii)

\cos A = \frac{4}{5}

(iii) tan θ = 11
(iv)

\sin θ = \frac{11}{15}

(v)

\tan α = \frac{5}{12}

(vi)

\sin θ = \frac{\sqrt{3}}{2}

(vii)

\cos θ = \frac{7}{25}

(viii)

\tan θ = \frac{8}{15}

(ix)

\cot θ = \frac{12}{5}

(x)

\sec θ = \frac{13}{5}

(xi)

cosec θ = \sqrt{10}

(xii)

\cos θ = \frac{12}{15}

Some trigonometric ratios and the interval in which $θ$ lies is given. Match the intervals with the ratios which are positive in those intervals.

$θ$ gives positive values

p. (0, $\frac{π}{2}$ ) 1. Only sin $θ$ , cosec $θ$

q. ( $\frac{π}{2}$ , $π$ ) 2. Only cos $θ$ , sec $θ$

r. $(π, \frac{3 π}{2})$ 3. Only tan $θ$ , cot $θ$

s. $(\frac{3 π}{2}, 2 π)$ 4. All sin $θ$ , cos $θ$ , tan $θ$ , cot $θ$ , sec $θ$ , cosec $θ$

Find the values of the other five trigonometric functions in each of the following:

$(i) c o s θ = \frac{12}{5}, θ$ in quadrant III

$(i i) c o s θ = - \frac{1}{2}, θ$ in quadrant II

$(i i i) t a n θ = \frac{3}{4}, θ$ in quadrant III

$(i v) s i n θ = \frac{3}{5}, θ$ in quadrant I

In the table, trigonometric ratios and the intervals of $θ$ are given. Match the intervals with the ratios which are positive in those intervals.

\begin{matrix} θ & gives positive values p. (0, \frac{π}{2}) & 1. Only sin θ, cosec θ q. (\frac{π}{2}, π) & 2. Only cos θ, sec θ r. (π, \frac{3 π}{2}) & 3. Only tan θ, cot θ s. (\frac{3 π}{2}, 2 π) & 4. All sin θ, cos θ, tan θ, cot θ, sec θ, cosec θ \end{matrix}

In the given figure,

∠

PQR = 90^°,

∠

PQS = 90^°,

∠

PRQ =

α

and

∠

QPS =

θ

Write the following trigonometric ratios.
(i) sin

α

, cos

α

, tan

α

(ii) sin

θ

, cos

θ

, tan

θ

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