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Home » Find the values of the following trigonometric ratios: (i) tan 7π/4 (ii) sin 17π/6
Find the values of the following trigonometric ratios: (i) tan 7π/4 (ii) sin 17π/6
CBSE | Class 11 | Exercise 5.3 | Maths | RD Sharma | Trigonometric Functions
Find the values of the following trigonometric ratios: (i) tan 7π/4 (ii) sin 17π/6

(i)

    \[tan\text{ }7\pi /4\]

 

    \[tan\text{ }7\pi /4\text{ }=\text{ }tan\text{ }{{315}^{o}}\]

    \[=\text{ }tan\text{ }{{\left( 90\times 3\text{ }+\text{ }45 \right)}^{o}}\]

Since,

    \[{{315}^{o}}\]

 lies in the

    \[IV\text{ }quadrant\]

in which tangent function is negative.

    \[tan\text{ }{{315}^{o}}~=\text{ }tan\text{ }{{\left( 90\times 3\text{ }+\text{ }45 \right)}^{o}}\]

    \[=\text{ }-\text{ }cot\text{ }{{45}^{o}}\]

    \[=\text{ }-1\]

 

(ii) 

    \[sin\text{ }17\pi /6\]

    \[sin\text{ }17\pi /6\text{ }=\text{ }sin\text{ }{{510}^{o}}\]

    \[=\text{ }sin\text{ }{{\left( 90\times 5\text{ }+\text{ }60 \right)}^{o}}\]

Since,

    \[{{510}^{o}}\]

 lies in the

    \[II\text{ }quadrant\]

in which sine function is positive.

    \[sin\text{ }{{510}^{o}}~=\text{ }sin\text{ }{{\left( 90\times 5\text{ }+\text{ }60 \right)}^{o}}\]

    \[=\text{ }cos\text{ }{{60}^{o}}\]

    \[=\text{ }1/2\]

i

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