Pythagoras Pythagoras' Theorem says that for a right angled triangle, the square of the long side equals the sum of the squares of the other two sides x 2 y 2 = 1 2 But 1 2 is just 1, so x 2 y 2 = 1 (the equation of the unit circle) Also, since x=cos and y=sin, we get (cos(θ)) 2 (sin(θ)) 2 = 1 a useful "identity" Important Angles 30°, 45° and 60° You should try to rememberDetermine angle type 240 is an obtuse angle since it is greater than 90° tan (240) = √ 3 In Microsoft Excel or Google Sheets, you write this function as =TAN (RADIANS (240)) Important Angle Summary θ° θ radians= 1 / 2√3 = (1 / 2√3) x (2√3 / 2√3) So, cot 15 0 = 2 √3 So, on putting the values of cot 15 0 and tan 15 0 in equation (i), we will get = (2 √3) 2 (2 √3) 2 = 4 3 2√3 4 3 2√3 = 14
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Simplify 1/2√3 2/√5√3 1/2√5 Maths NCERT Solutions;Mathx = \dfrac{\sqrt{31}}{2} \tag {E01}/math math\implies 2x = \sqrt{3}1 \implies (2x1) = \sqrt{3} \tag {E02} /math math\text{Squaring }(2x1)^2 = 3 If sin1 x cot1 (1/2) = π/2, then x is equal to (a) 1/2 (b) 1/√5 (c) 2/√5 (d) √3/2 Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queries
√3)/2 = is a nonterminating and nonrecurring decimal and therefore is an irrational number (B) (√2 √3)/2 Exercise 12 Page No 6 1 Let x and y be rational and irrational numbers, respectively Is x y necessarily an irrational numberIf tanθ=√(3/2), then sum of the infinite series 12(1cosθ)3〖(1cosθ)〗^24〖(1cosθ)〗^3 ∞ is (a) 2/3 (b) √3/4 (c) 5/(2√2) (d) 5/2To buy(x^2) 5 e estão em PA,nesta ordemDetermine o perimetro do mesmo triângulo Measures on the sides of a triangle are exorced by x 1;2 x;
Ex 33, 5Find the value ofsin 75°sin 75° = sin (45° 30°) = sin 45° cos 30° cos 45° sin 30° = 1/√2 × √3/2 1/√2 × 1/2 = 1/√2 (√3/2 " " 1/2) = (√𝟑 𝟏)/(𝟐√𝟐) sin (x y) = sin x cos y cos x sin yPutting x = 45° and y = 30°Ex 33, 5Find the value of3 Chapter 1 c2 1 2 ( √ 3 ) 2 4 ⇒ c √ 4 2 d2 1 2 2 2 5 ⇒ d √ 5 e2 1 2 (√ 5 ) 2 6 ⇒ e √ 6 f 2 1 2 ( √ 6 ) 2 7 ⇒ f √ 7 g2 1 2 ( √ 7 ) 2 8 ⇒ g √ 8 2 √ 2 The length of "c" is a rational number 13 Since the length of the carpet equals the sum of the heightWrite sin (81) in terms of cos Since 81° is less than 90, we can express this in terms of a cofunction sin (θ) = cos (90 θ) sin (81) = cos (90 81) sin (81) = cos (9) In Microsoft Excel or Google Sheets, you write this function as =SIN (RADIANS (81))
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Next consider 30° and 60° angles In a 30°60°90° right triangle, the ratios of the sides are 1 √3 2 It follows that sin 30° = cos 60° = 1/2, and sin 60° = cos 30° = √3 / 2 Prove that (i) tan 225 ° cot 405 ° tan 765 ° cot 675 ° = 0 (ii) sin 8π/3 cos 23π/6 cos 13π/3 sin 35π/6 = 1/2 (iii) cos 24 ° cos 55 ° cos 125 ° cos 4 ° cos 300 ° = 1/2 (iv) tan (125 °) cot (405 °) – tan (765 °) cot (675 °) = 0 (v) cos 570 ° sin 510 ° sin (330 °) cos (390 °) = 0 (vi) tan 11π/3 – 2 sin 4π/6 – 3/4 cosec 2 π/4 4 cos 2 17π/6Calculate cos(16)° Determine quadrant Since our angle is between 0 and 90 degrees, it is located in Quadrant I In the first quadrant, the values for sin, cos and tan are positive
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Sin(15) cos(15) = sin(45 30) cos(45 30) = sin(45)cos(30) cos(45)sin(30) cos(45)cos(30) sin(45)sin(30) = (1/√2)(√3/2) (1/√2)(1/2) (1/√2)(√3>Sequences and series > Geometric progression Geometric progression > 1 √(2)12 (3) 3 2√(2) 1 √(2)12 (3) 3 2√(2)(x ^ 2)5 and are in P A, in this order Determine the perimeter of the same triangle Translated 6
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So if you recall, the short leg is 1/2 the hypotenuse, so the ycoordinate is 1/2, and the long leg is √3 times the shorter leg, or (√3)/2, so the xcoordinate is (√3)/2 The coordinates of that point are ((√3)/2,1/2) Now use the identities in the previous step to find thatA special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90° This is called an "anglebased" right triangle A "sidebased" right triangle is one in which the lengths of the sides form ratios ofP C T 0° 0 0 1 0 − 30° π 6 1 2 √3 2 √3 3 √3 45° π 4 √2 2 √2 2 1 1 60° π 3 √3 2 1 2 √3
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If P = (√3/2, 1/2), (1/2, √3/2), A = (1, 1), (0, 1) and Q = PAPT, then PTQ05 P is Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queries If i =√1, then 4 5(1/2 i√3/2)334 3(1/2 i√3/2)365 is equal to (a) 1 i√3 (b) 1 i√3 (c) i√3 (d) i√3We thoroughly check each answer to a question to provide you with the most correct answers Found a mistake?
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