In the given figure- - PQR -90- - PQS -90- - PRQ - and - QPS - Write the following trigonometric ratios-i sin- cos- tan-ii sin- cos- tan-

(i) sinα = nbsp;Opposite nbsp;side nbsp;of nbsp;∠PRQHypotenuse=PQPR cosα nbsp;= nbsp;Adjacent nbsp;side nbsp;of nbsp;∠PRQHypotenuse=RQPR t ...

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Byju's Answer

Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

In the given ...

Question

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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Solution

(i)
sin $α$ = $\frac{Opposite side of ∠ PRQ}{Hypotenuse} = \frac{PQ}{PR}$

cos $α$ = $\frac{Adjacent side of ∠ PRQ}{Hypotenuse} = \frac{RQ}{PR}$

tan $α$ = $\frac{Opposite side of ∠ PRQ}{Adjacent side of ∠ PRQ} = \frac{PQ}{RQ}$

(ii)
sinθ = $\frac{Opposite side of ∠ QPS}{Hypotenuse} = \frac{QS}{PS}$

cosθ = $\frac{Adjacent side of ∠ QPS}{Hypotenuse} = \frac{PQ}{PS}$

tanθ = $\frac{Opposite side of ∠ QPS}{Adjacent side of ∠ QPS} = \frac{QS}{PQ}$

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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}

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) $c o s θ = \frac{12}{15}$

In the figure below, if $∠$ PQR = $∠$ PRQ, then, which of the following is/are true?

Q. If

s i n θ = \frac{a}{\sqrt{a^{2} + b^{2}}}, 0 < θ < 90^{\circ}

, find the values of

c o s θ

and

t a n θ

Q. PQRS is a cyclic quadrilateral. Given

∠

QPS

= 73^{o}

∠

PQS

= 55^{o}

and

∠

PSR

= 82^{o}

, calculate

∠

PRQ.

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In the given figure, ∠PQR = 90° , ∠PQS = 90° , ∠PRQ = α and∠QPS = θ Write the following trigonometric ratios. (i) sinα, cosα , tanα (ii) sinθ, cosθ, tanθ

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 $θ$