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JEE • MATHEMATICS • TRIGONOMETRY RATIOS

Trigonometry ratios practice · Medium

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Showing 151-157 of 157 questions

151 Medium

151 of 157

Application +4 | -1

The value of

\sin \,\,\frac{\pi }{{16}}\,\,\sin \,\,\frac{{3\pi }}{{16}}\,\,\sin \,\,\frac{{5\pi }}{{16}}\,\,\sin \,\,\frac{{7\pi }}{{16}}

View answer and explanation

Correct option: A

\frac{{\sqrt 2 }}{{16}}

Option A (

\frac{{\sqrt 2 }}{{16}}

) is correct because the product of the sines can be simplified using trigonometric identities to obtain this value.

152 Medium

152 of 157

Remembering +4 | -1

\sum_{n=12}^4 \sin \left(\frac{\pi}{2}\right)

is equal to

View answer and explanation

Correct option: D

\frac{\sqrt{3}+\sqrt{2}+2}{2}

Option D (

\frac{\sqrt{3}+ \sqrt{2}+2}{2}

) is correct because it is the sum of

\sin{\frac{\pi}{1}}

\sin{\frac{\pi}{2}}

\sin{\frac{\pi}{3}}

, and

\sin{\frac{\pi}{4}}

153 Medium

153 of 157

Application +4 | -1

\tan A, \tan B, \tan C

are the roots of the cubic equation

x^3-7 x^2+11 x-7=0

then

A+B+C=

View answer and explanation

Correct option: B

\pi

Option B (

\pi

) is correct because the sum of the roots of the cubic equation gives the tangent of the sum of the angles, which equals zero, implying the sum of the angles is

\pi

154 Medium

154 of 157

Analyzing +4 | -1

In a

\triangle A B C, \cos B \cdot \cos C+\sin B \cdot \sin C \cdot \sin ^2 A=1

Then, the triangle is

View answer and explanation

Correct option: A

right angled isosceles

Option A (right angled isosceles) is correct because the given equation implies that

B=C

and

A = \frac{\pi}{2}

, making the triangle right-angled and isosceles.

155 Medium

155 of 157

Application +4 | -1

\sin \theta=\frac{12}{13}\left(0 < \theta < \frac{\pi}{2}\right)

and

\cos \phi=-\frac{3}{5},\left(\pi < \phi < \frac{3 \pi}{2}\right)

Then

\sin (\theta+\phi)

will be

View answer and explanation

Correct option: B

\frac{-56}{65}

Option B (

\frac{{-56}}{{65}}

) is correct because it is obtained by correctly applying the sine addition formula and considering the quadrant of

\phi

156 Medium

156 of 157

Analyzing +4 | -1

The value of

{\cos ^2}A\;{\left( {3 - 4\,\,{{\cos }^2}A} \right)^2} + {\sin ^2}A\;{\left( {3 - 4\,\,{{\sin }^2}\,A} \right)^2}

is equal to

View answer and explanation

Correct option: C

\mathrm{1}

Option C (1) is correct because the expression simplifies to 1 after applying trigonometric identities and algebraic manipulation.

157 Medium

157 of 157

Application +4 | -1

\;\tan \,\,\mathrm{\theta },\,\,2\tan \mathrm{\theta } + 2,\;\,3\tan \mathrm{\theta } + 3\;

are in GP, then the value of

\frac{{7 - 5\,\cot \mathrm{\theta }}}{{9 - 4\,\sqrt {{{\sec }^2}\mathrm{\theta } - 1} }}

View answer and explanation

Correct option: C

\frac{{33}}{{100}}

Option C (33/100) is the correct answer because it is obtained by solving the given GP condition for tan θ and substituting it into the expression.

Revision notes and key takeaways

Review TRIGONOMETRY RATIOS in your textbook or class notes, then use this set to check your understanding.

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