11th Maths Monthly Test- 3 (Trigonometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test- 3 (Trigonometry) -Aug 2020

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

If the arcs of same lengths in two circles subtend central angles 30° and 80⁰, find the ratio of their radii.

Find the value of tan\(\frac { \pi }{ 2 } \).

Express each of the following as a product.
sin 75^o - sin 35^o

Find the values of cos(300°).

Identify the Quadrant in which a given measure lies; -55⁰

Find the general solution of \(\sqrt { 3 } \) sec2x=2

If (-2, -3) is a point on the terminal side of \(\theta\) . Find all the trigonometrical ratios.

If the slides of \(\triangle\) ABC are a = 4, b = 6, C = 8 then show that 4 cos B + 3 cos C = 2

Find the values of cos 2A, A lies in the first quadrant, when cos A = \(\frac{15}{17}\)

Suppose that a satellite in space, an earth station and the centre of earth all in the same plane. Let r be the radius of earth and R be the distance from the centre of earth to the satellite. Let d be the distance from the earth station to the satellite. Let 30 be the angle of elevation from the earth station to the satellite. If the line segment connecting earth station and satellite substends angle at the centre of earth, then prove that d=\(\sqrt { 1+\left( \frac { r }{ R } \right) ^{ 2 }-2\frac { r }{ R } cos\alpha } \) .

Prove that \(\sin { \left( \pi +\theta \right) } =-\sin { \theta } \)

Express the following angles in radian measure; 150⁰

Convert:6 radians to degrees.

Find the value of \(\sqrt 3 cosec20^0-sec20^0\).

Part - B

Generic 3 - Answer All Question

Prove that 4 cos 12° cos 48° cos 72° = cos 36°

Find the values of other five trigonometric functions for the following
Given cos \(\theta\) = \(\frac { 2 }{ 3 } \) \(\theta\) lies in the I quadrant

Solve: tan²θ+(1-\(\sqrt3\))tanθ-\(\sqrt3\)=0

In a \(\triangle \)ABC, prove that a cosA+bcos B+c cos C=2a sin B sin C

Find the principal solution of cos \(\theta ={1\over 2}\)

A rope of length 12 m is given. find the largest area of the triangle formed by this rope and find the dimensions of the triangle So formed

Prove that sin (270° - \(\theta\)) sin (90° - \(\theta\)) - cos (270° - \(\theta\)) cos (90° + \(\theta\)) + 1 = 0.

Show that \(\cot { \left( 7\frac { 1° }{ 2 } \right) } =\sqrt { 2 } +\sqrt { 3 } +\sqrt { 4 } +\sqrt { 6 } \)

Prove that cos 20° cos 40° cos 80° = \(\frac{1}{8}.\)

Find the principal value of \(sin^{ -1 }\left( \frac { 1 }{ \sqrt { 2 } } \right) \).

Derive projection formula From; law of sines

Prove that \({{cos\ 2\ x}\over{1+sin\ 2x}}=tan\left( {{\pi}\over{4}}-x \right)\)

\(a\cos { x+b\sin { x } } =m\) and \(a\sin { x } -b\cos { x } =n\), prove that \({ a }^{ 2 }+{ b }^{ 2 }={ m }^{ 2 }+{ n }^{ 2 }\)

In a \(\triangle \)if cos C=\(\frac { sinA }{ 2sinB } \)show that the triangle is isosceles.

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11th Maths Monthly Test- 3 (Trigonometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test- 3 (Trigonometry) -Aug 2020

Part - A

Generic 2 - Answer All Question

If the arcs of same lengths in two circles subtend central angles 30° and 800, find the ratio of their radii.

Find the value of tan\(\frac { \pi }{ 2 } \).

Express each of the following as a product. sin 75o - sin 35o

Find the values of cos(300°).

Identify the Quadrant in which a given measure lies; -550

Find the general solution of \(\sqrt { 3 } \) sec2x=2

If (-2, -3) is a point on the terminal side of \(\theta\) . Find all the trigonometrical ratios.

If the slides of \(\triangle\) ABC are a = 4, b = 6, C = 8 then show that 4 cos B + 3 cos C = 2

Find the values of cos 2A, A lies in the first quadrant, when cos A = \(\frac{15}{17}\)

Prove that \(\sin { \left( \pi +\theta \right) } =-\sin { \theta } \)

Express the following angles in radian measure; 1500

Convert:6 radians to degrees.

Find the value of \(\sqrt 3 cosec20^0-sec20^0\).

Part - B

Generic 3 - Answer All Question

Prove that 4 cos 12° cos 48° cos 72° = cos 36°

Find the values of other five trigonometric functions for the following Given cos \(\theta\) = \(\frac { 2 }{ 3 } \) \(\theta\) lies in the I quadrant

Solve: tan2θ+(1-\(\sqrt3\))tanθ-\(\sqrt3\)=0

In a \(\triangle \)ABC, prove that a cosA+bcos B+c cos C=2a sin B sin C

Find the principal solution of cos \(\theta ={1\over 2}\)

A rope of length 12 m is given. find the largest area of the triangle formed by this rope and find the dimensions of the triangle So formed

Prove that sin (270° - \(\theta\)) sin (90° - \(\theta\)) - cos (270° - \(\theta\)) cos (90° + \(\theta\)) + 1 = 0.

Show that \(\cot { \left( 7\frac { 1° }{ 2 } \right) } =\sqrt { 2 } +\sqrt { 3 } +\sqrt { 4 } +\sqrt { 6 } \)

Prove that cos 20° cos 40° cos 80° = \(\frac{1}{8}.\)

Find the principal value of \(sin^{ -1 }\left( \frac { 1 }{ \sqrt { 2 } } \right) \).

Derive projection formula From; law of sines

Prove that \({{cos\ 2\ x}\over{1+sin\ 2x}}=tan\left( {{\pi}\over{4}}-x \right)\)

\(a\cos { x+b\sin { x } } =m\) and \(a\sin { x } -b\cos { x } =n\), prove that \({ a }^{ 2 }+{ b }^{ 2 }={ m }^{ 2 }+{ n }^{ 2 }\)

In a \(\triangle \)if cos C=\(\frac { sinA }{ 2sinB } \)show that the triangle is isosceles.

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Tamilnadu Stateboardszs - Class

If the arcs of same lengths in two circles subtend central angles 30° and 80⁰, find the ratio of their radii.

Express each of the following as a product.
sin 75^o - sin 35^o

Identify the Quadrant in which a given measure lies; -55⁰

Express the following angles in radian measure; 150⁰

Find the values of other five trigonometric functions for the following
Given cos \(\theta\) = \(\frac { 2 }{ 3 } \) \(\theta\) lies in the I quadrant

Solve: tan²θ+(1-\(\sqrt3\))tanθ-\(\sqrt3\)=0