If tan-43- then sin- is equal toa -45 but not 45b -45 or 45c 45 but not -45d none of these

Given nbsp;tan nbsp;θ= 43 Since tan is negative in 2nd or 4th quadrant nbsp; ⇒ θ lies in 2nd or 4th quadrant Since AC2 = AB2 + BC2 = (–4)2 + (3)2 AC2 n ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

If tanθ=-43, ...

Question

If $\tan θ = - \frac{4}{3},$ then sin θ is equal to

(a) $- \frac{4}{5}$ but not $\frac{4}{5}$

(b) $- \frac{4}{5}$ or $\frac{4}{5}$

(c) $\frac{4}{5}$ but not $- \frac{4}{5}$

(d) none of these

Open in App

Solution

Given $\tan θ = - \frac{4}{3}$
Since tan is negative in 2nd or 4th quadrant
⇒ θ lies in 2nd or 4th quadrant

Since AC² = AB² + BC² = (–4)² + (3)²
AC² = 25
AC = ± 5
i.e. AC = 5
$∴ sinθ = - \frac{4}{5} or \frac{4}{5}$
Hence, the correct answer is option B.

Suggest Corrections

Similar questions

Q. If θ and 2θ − 45° are acute angles such that sin θ = cos (2θ − 45°), then tan θ is equal to

(a) 1
(b) −1
(c)

\sqrt{3}

(d)

\frac{1}{\sqrt{3}}

Q. If

\to A = 2^i + 4^j - 5^k

the direction of cosines of the vector

\to A

are

Q. If

sin θ = cos (2 θ - 45^{\circ}), 0 < (2 θ - 45^{\circ}) < 90^{\circ},

then

tan θ

Q. If

\tan θ = \frac{4}{5}

, find the value of

\frac{\cos θ - \sin θ}{\cos θ + \sin θ}

If in $△ A B C \frac{2 c o s A}{a} + \frac{c o s B}{b} + \frac{2 c o s C}{c} = \frac{a}{b c} + \frac{b}{c a} = t h e n ∠ A$ is equal to

Join BYJU'S Learning Program

If tan θ=-43, then sin θ is equal to (a) -45 but not 45 (b) -45 or 45 (c) 45 but not -45 (d) none of these

Given tan θ=-43 Since tan is negative in 2nd or 4th quadrant ⇒ θ lies in 2nd or 4th quadrant Since AC2 = AB2 + BC2 = (–4)2 + (3)2 AC2 = 25 AC = ± 5 i.e. AC = 5 ∴ sinθ=-45 or 45 Hence, the correct answer is option B.

If $\tan θ = - \frac{4}{3},$ then sin θ is equal to

(a) $- \frac{4}{5}$ but not $\frac{4}{5}$

(b) $- \frac{4}{5}$ or $\frac{4}{5}$

(c) $\frac{4}{5}$ but not $- \frac{4}{5}$

(d) none of these

Given $\tan θ = - \frac{4}{3}$
Since tan is negative in 2nd or 4th quadrant
⇒ θ lies in 2nd or 4th quadrant

Since AC² = AB² + BC² = (–4)² + (3)²
AC² = 25
AC = ± 5
i.e. AC = 5
$∴ sinθ = - \frac{4}{5} or \frac{4}{5}$
Hence, the correct answer is option B.