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Apr 11, 2016 · Since sin(π 12) is positive, then only the positive answer is accepted. sin(π 12) = √2 −√3 2. Check by calculator. Calculator --> sin(π 12) = sin15∘ = 0.26. √2 −√3 2 = √0.27 2 = 0.52 2 = 0.26. OK. Answer link. 1/4 (sqrt6 - sqrt2) >We want to find replacement angles for pi/12" that will produce exact values " These must come ...
Jul 2, 2016 · sin(pi/5)=sqrt(10-2sqrt5)/4 Let theta=pi/5, then 5theta=pi and 3theta=pi-2theta. Note theta) is an acute angle. Hence sin3theta=sin(pi-2theta) but as sin(pi-A)=sinA This can be written as sin3theta=sin2theta expanding them or 3sintheta-4sin^3theta=2sinthetacostheta as theta=pi/5 we have sintheta!=0 and dividing by it we get 3-4sin^2theta=2costheta or 3-4(1-cos^2theta)=2costheta or 4cos^2theta-2costheta-1=0 and using quadratic formula costheta=(2+-sqrt(2^2-4*4*(-1)))/(2*4) = (2+-sqrt(20))/8 ...
Nov 1, 2017 · As #pi/24=180^@/24=(7 1/2)^@#, let us first work out #cos(pi/12)# or #cos15^@#. #cos15^@=cos(45^@-30^@)# = #cos45^@cos30^@+sin45^@sin30^@#
Apr 17, 2018 · Find the value of sinπ/14 × sin3π/14 × sin5π/14 × sin7π/14 × sin9π14 × sin11π/14 × sin13π/14 ?
Jul 27, 2016 · What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#?
Feb 27, 2017 · sin (pi/8) = sqrt(2 - sqrt2)/2 Use trig identity: 2sin^2 a = 1 - cos 2a In this case, a = pi/8 and 2a = pi/4 --> cos pi/4 = sqrt2/2 --> 2sin^2 (pi/8) = 1 - sqrt2/2 ...
Apr 15, 2015 · How do you use the sum and difference identities to find the exact value of tan 105 degrees? How do you apply the sum and difference formula to solve trigonometric equations? How do you evaluate #sin(45)cos(15)+cos(45)sin(15)#?
Feb 11, 2016 · If you don't know the trigonometric circle, you can see that if one of the small angles of a rectangle triangle is pi/4, the other will be also pi/4, which implies the catets are equal. So if x=y, you will have x^2+y^2=1 2y^2=1 y^2=1/2 y=sqrt (1/2)=sqrt (2)/2 To get the sin of pi/4 you divide the opposite catet (sqrt (2)/2) by the hypothenuse ...
Aug 29, 2015 · By the Pythagorean Theorem, the height (the side opposite the angle of π 3) will have a length of √3. sin(π 3) = side opposite π 3 hypotenuse = √3 2. sin (pi/3) = sqrt (3)/2 Consider the series of diagrams below. The interior angles of a triangle always add up to pi radians An equilateral triangle will have all three angles = pi/3 and ...
Apr 27, 2018 · The fastest way is to look at the trig table, titled "Trig Functions of Special Arcs". This table gives --> sin(π 6) = 1 2. Second method. 1/2 For trigonometry, it is imperative to memorize a tool known as the Unit Circle. This is a circle with a radius of 1 and a center on the origin. The points on the circumference of the circle are the ...
