ASSIGNMENT ON TRIGONOMETRY LEVEL 1 (CBSE/NCERT/STATE BOARDS) Find the degree measure corresponding to the following radian measures :

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1 ASSIGNMENT ON TRIGONOMETRY LEVEL 1 (CBSE/NCERT/STATE BOARDS) Find the degree measure corresponding to the following radian measures : (i) c 1 (ii) - c (iii) 6 c (iv) c Find the length of an arc of a circle of radius cm subtending a central angle measuring 1. In a circle of diameter 0 cm the length of a chord is 0 cm. Find the length of minor arc corresponding to the chord. The angles of a triangle are in A.P. The number of degrees in the least is to the number of radians in the greatest as 60 :. Find the angles in degrees. A circular wire of radius 7. cm is cut and bent so as to lie along the circumference of a hoop whose radius is 10 cm. Find the degrees the angle which is subtended at the centre of the hoop. If the angular diameter of the moon be 0', how far from the eye a con of diameter. cm be kept of hide the moon? The angle in one regular polygon is to that in another as : and the number of sides in first is twice that in the second. Determine the number of sides of two polygons. Find the diameter of the sun in km supposing that it subtends an angles of ' at the eye of an observer. Given that the distance of the sun is km. Find the values of cos and tan if sin = Find all other trigonometric ratios of sin = and < <. 6 and lies in quadrant III. If sec and < <, find the value of 1 tan cos ec. 1 cot cos ec 1

2 1 sin 1 sin sec tan, sec tan, if if If sin 1 + sin + sin =, then write the value of cos 1 + cos + cos. If sin + cos =, then write the value of sin - cos. Write the value of (sin 6 + cos 6 ) (sin + cos ) + 1. If sin x + sin x = 1, then write the value of cos 8 x + cos 6 x + cos x. If sin x + cosec x =, then write the value of sin n x + cosec n x. 1 cos cos ec cot, 1 cos cos ec cot, if 0 if If sin, 1 tan and < < < <, find the value of 8 tan - sec. cos 10 cos 0 + sin 90 cos 10 = -1. sin(-0) (cos 90) + cos(-660) (sin 0)= -1 If A, B, C, D are angles of a cyclic quadrilateral, prove that cos A + cos B + cos C + cos D = 0. (i) tan cot 0 + tan 76 cot 67 = 0 (ii) cos + cos + cos 1 + cos 0 + cos 00 = (iii) tan sin cos ec cos 6 6 (iv) sin sec sin cot If A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos (180 - A) + cos (180 + B) + cos (180 + C) sin (90 + D) = 0

3 Find x from the following equations : (i) cosec (90 + ) + x cos cot (90 + ) = sin (90 + ) (ii) x cot (90 + ) + tan (90 + ) sin + cosec (90 + ) = 0 If 1 cot, sec, where < < and < <. Find the value of tan( + ). State the quadrant in which + terminates. Find the sign of the expression sin cos 100. Prove that tan 7 + cot 7 = sin(b C) sin(c A) sin(a B) 0 cos BcosC cosccos A cos Acos B If cos ( - ) + cos ( - ) + cos ( - ) = cos + cos + cos = sin + sin + sin = 0, prove that : (i) tan A tan A tan A = tan A tan A tan A (ii) cot A cot A cot A cot A cot A cot A = 1 If and are acute angles such that. m tan m1 and 1 tan, prove that m 1 A A 1 sin sin sin A 8 8 If cos ( + ) =, sin ( - ) and, lie between 0 and, prove that 1 6 tan. 1 If tan ( cos ) = cot ( sin ), prove that cos

4 If sin + sin = a and cos + cos = b, show that (i) b cos( ) b a a ab (ii) sin( ) a b 9 cos cos cos cos cos 0 cos 0 cos 60 cos 80 = 1 16 sin 10 sin 0 sin 0 sin 70 = tan 0 tan 0 tan 80 = tan 60 Prove that sin A sin (60 - A) sin (60 + A) = 1 sin A If + = 90, find the maximum and minimum values of sin sin. Show that : (i) sin A sin (B C) + sin B sin(c A) + sin C sin(a B) = 0 (ii) sin(b C) cos (A D) + sin (C A) cos (B D) + sin (A B) cos (C D) = 0 cos + cos + cos + cos( + + ) = cos cos cos sin A sina sina sin 7A tan A cos A cosa cosa cos 7A cos AcosA cos Acos7A cos Acos10A cot 6Acot A sin AsinA sin AsinA sin Asin 7A n n n AB cos A cos B sin A sin B cot, if n is even sin A sin B cos A cos B 0, if n is odd

5 sin( ) sin sin( ) tan cos( ) cos cos( ) (i) sin + sin + sin - sin ( + + ) = sin sin sin (ii) cos (A + B + C) + cos (A B + C) + cos (A + B C) + cos (-A + B + C) = cos A cos B cos C Show that : cos8 cos sec8 1 tan8 sec 1 tan If, then write the value of 1cos. If < < 1cos, then write the value of 1cos cos 1 cos 1 cos 1 cos (i) sinx sinx sin x tan x cosx cos x x (ii) sin x + sin x + sin 6x = cos x sin Show that cosec 0 - sec 0 = If sin A =, where 0 < A < 90, find the values of sin A, cos A, tan A and sin A Find the value of sin sin sin tan + tan + tan + 8 cot 8 = cot tan tan sec

6 If sin = and cos = 1, prove that 8 cos 6 cos A cos(60 A) cos (60 + A) = 1 cosa If cos + cos + cos = 0, then prove that cos + cos + cos = 1 cos cos cos cos A = 16 cos A 0 cos A + cos A 6