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Standard XII

Mathematics

Sin(A+B)Sin(A-B)

Which trigono...

Question

Which trigonometric function is positive in third quadrant,

sin θ

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tan θ

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cos θ

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sec θ

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Solution

The correct option is B $tan θ$
Given :Trigonometry ratios, i.e,
$sin θ, tan θ, cos θ, sec θ$
To find: Positive ratio in 3rd quadrant
Solution: We know that third quadrant range is $180^{0}$ to $270^{0}$ and tangent and cotangent is positive in third quadrant.
Hence, answer is $tan θ$ , option - B

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Similar questions

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

Q. Find the values of the other five trigonometric functions in each of the following:
(i)

\cot θ = \frac{12}{5},

θ in quadrant III
(ii)

\cos θ = - \frac{1}{2},

θ in quadrant II
(iii)

\tan θ = \frac{12}{5},

θ in quadrant III
(iv)

\sin θ = \frac{3}{5},

θ in quadrant I

Q. Find the values of other trigonometric function

(sin, cos, tan)

in each of the following problems
i)

sin θ = 3 / 5 : θ

I^{s t}

quadrant
ii)

cos θ = - 1 / 2 : θ

I I^{s t}

quadrant
iii)

sin θ = 3 / 4 : θ

I I I^{s t}

quadrant$

Q. Find the quadrant in which

θ

lies, if
(i)

cos θ

is negative but

sin θ

is positve
(ii)

sin θ

is negative but

tan θ

is positive
(iii)

cos θ

is negative and

sin θ

is negative
(iv)

cos θ

and

cot θ

are both negative
(v)

sec θ

is positive but

c o sec θ

is negative

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 $θ$

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Which trigonometric function is positive in third quadrant,

The correct option is B tanθGiven :Trigonometry ratios, i.e,sinθ,tanθ,cosθ,secθTo find: Positive ratio in 3rd quadrantSolution: We know that third quadrant range is 1800 to 2700 and tangent and cotangent is positive in third quadrant.Hence, answer is tanθ, option - B