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What does sin(pi/4) = ?
Let's consider a special right triangle: the 45-45-90 triangle.
In any 45-45-90 triangle, since the two 45 degree angles are congruent, the sides opposite to those angles are both congruent.
Now, considering the unit circle, the radius of the circle must be one.
So, if you put in a 45-45-90 triangle in a unit circle, this allows you to find the value of sin pi/4 because pi/4 radians = 45 degrees.
Because the circle has radius 1, the hypotenuse of the triangle must also be one. Since the other two sides must be equal, you can solve for them using the Pythagorean theorem.
a2 + b2 = c2
a2 + a2 = 12
2a2 = 1
a2 = 1/2
a = √(1/2)
a = 1/√(2) * (√(2)/√(2))
a = √(2) / 2
Since sin is defined as opp/hyp, sin 45 degrees (pi/4 radians) = (√(2)/2)/1 = √(2)/2
I hope this helped explain my answer. If there's anything that's still confusing, just tell me. (Sorry I didn't do it the first time).
What else can I help you with?
When does cotangent equal -1?
cot[x]= -1 cot[x] = cos[x] / sin[x] cos[x] / sin[x] = -1 cos[x] = -sin[x] |cos[x]| = |sin[x]| at every multiple of Pi/4 + Pi/2. However, the signs disagree at 3Pi/4 + nPi, where n is an integer.
How do you calculate sinpi on 7?
Do you mean Sin(pi/7) or {Sin(pi)} / 7 Note the position of the '7' be it inside or outside the Sine Function. Clarity is needed, in the position of the '7'. However, Maker sure you calculator is in 'Radian' mode. Sin(pi/7) = Sin(0.44879895...) =0.0078329.... or {Sin(pi)}/7 = 0.054803665.../7 = 0.007829095021.... Note the two different answers.
What is the derivative of sin pi x?
If you mean y = Sin(pi(x)) Then Use the chain rule dy/dx = dy/du X du/dx Let pi(x) = u y = Sin (u) dy/du = Cos(u) u = pi(x) du/dx = pi Combining dy/dx = pi Cos(u) = piCos (pi(x)). The answer!!!!!
Sin x degrees equals 4 over 15 what would the value of x be?
x = sin-1 (4/15) ( sin -1 is [SHIFT] [sin] on a calculator ) = 15.5
How do you determine the sign of a sine curve?
For 0 < x < pi. sin(x) is positive,for pi < x < 2*pi, sin(x) is negative and these intervals can be left or right-shifted by any multiple of 2*pi radians.
What is the exact value of the expression cos 7pi over 12 cos pi over 6 -sin 7pi over 12 sin pi over 6?
cos(a)cos(b)-sin(a)sin(b)=cos(a+b) a=7pi/12 and b=pi/6 a+b = 7pi/12 + pi/6 = 7pi/12 + 2pi/12 = 9pi/12 We want to find cos(9pi/12) cos(9pi/12) = cos(3pi/4) cos(3pi/4)= cos(pi-pi/4) cos(pi)cos(pi/4)-sin(pi)sin(pi/4) cos(pi)=-1 sin(pi)=0 cos(pi/4) = √2/2 sin(pi/4) =√2/2 cos(pi)cos(pi/4)-sin(pi)sin(pi/4) = - cos(pi/4) = -√2/2
What is the sin pi over 4?
sin(pi/4) and cos(pi/4) are both the same. They both equal (√2)/2≈0.7071■
What is the exact value using a sum or difference formula of the expression cos 11pi over 12?
11pi/12 = pi - pi/12 cos(11pi/12) = cos(pi - pi/12) cos(a-b) = cos(a)cos(b)+sin(a)sin(b) cos(pi -pi/12) = cos(pi)cos(pi/12) + sin(pi)sin(pi/12) sin(pi)=0 cos(pi)=-1 Therefore, cos(pi -pi/12) = -cos(pi/12) pi/12=pi/3 -pi/4 cos(pi/12) = cos(pi/3 - pi/4) = cos(pi/3)cos(pi/4)+sin(pi/3) sin(pi/4) cos(pi/3)=1/2 sin(pi/3)=sqrt(3)/2 cos(pi/4)= sqrt(2)/2 sin(pi/4) = sqrt(2)/2 cos(pi/3)cos(pi/4)+sin(pi/3) sin(pi/4) = (1/2)(sqrt(2)/2 ) + (sqrt(3)/2)( sqrt(2)/2) = sqrt(2)/4 + sqrt(6) /4 = [sqrt(2)+sqrt(6)] /4 Therefore, cos(pi/12) = (sqrt(2)+sqrt(6))/4 -cos(pi/12) = -(sqrt(2)+sqrt(6))/4 cos(11pi/12) = -(sqrt(2)+sqrt(6))/4
Y equals 4 sin x for x equals pi?
sin(pi) = 0 so 4*sin(pi) = 0 so Y = 0
How was it determined that the tangent of pi divided by 4 is 1?
As tan(x)=sin(x)/cos(x) and sin(pi/4) = cos(pi/4) (= sqrt(2)/2) then tan(pi/4) = 1
Sin x - cos x 0 0?
sin x - cos x = 0sin x = cos x(sin x)^2 = (cos x)^2(sin x)^2 = 1 - (sin x)^22(sin x)^2 = 1(sin x)^2 = 1/2sin x = ± √(1/2)sin x = ± (1/√2)sin x = ± (1/√2)(√2/√2)sin x = ± √2/2x = ± pi/4 (± 45 degrees)Any multiple of 2pi can be added to these values and sine (also cosine) is still ± √2/2. Thus all solutions of sin x - cos x = 0 or sin x = cos x are given byx = ± pi/4 ± 2npi, where n is any integer.By choosing any two integers , such as n = 0, n = 1, n = 2 we can find some solutions of sin x - cos x = 0.n = 0, x = ± pi/4 ± (2)(n)(pi) = ± pi/4 ± (2)(0)(pi) = ± pi/4 ± 0 = ± pi/4n = 1, x = ± pi/4 ± (2)(n)(pi) = ± pi/4 ± (2)(1)(pi) = ± pi/4 ± 2pi = ± 9pi/4n = 2, x = ± pi/4 ± (2)(n)(pi) = ± pi/4 ± (2)(2)(pi) = ± pi/4 ± 4pi = ± 17pi/4
What is sin of -pi?
sin(-pi) = sin(-180) = 0 So the answer is 0
What is sin of 3 pi over 2?
Sin(3pi/2) = Sin(2pi - pi/2) Double angle Trig. Identity. Hence Sin(2pi)Cos(pi/2) - Cos(2pi) Sin(pi/2) Sin(2pi) = 0 Cos(pi/2) = 0 Cos(2pi) = 1 Sin(pi/2) = 1 Substituting 0 x 0 - 1 x 1 = 0 - 1 = -1 The answer!!!!!
What is the sin of pi?
sin(pi) = 0
What are the distinct fourth root of -1?
The four roots are cos(theta)+i*sin(theta) where theta = pi/4, 3*pi/4, 5*pi/4 and 7*pi/4.
What is the sin of pi divided by 2?
Do you mean Sin(pi/2) = 1 or [Sin(pi)] /2 = 0.0274....
What is the value of sin 3 pi over 2?
sin(3π/2) = -1
