0
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).
Add your answer:
Earn +20 pts
What is the derivative of sin pi x?
pi cos(pi x)
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.
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.
6 trigonometric values of 315 degrees?
To find exact values, you should use the unit circle.It is good practice, too, to use radians as this is much more helpful in higher levels of math, so, do yourself a favor and learn how to convert degrees into radians and start thinking about the circle in radians instead of degrees.315 degrees = (7 [Pi])/4 radiansYou can use the following conversion to find this: 90 degrees = Pi / 2 radians.315 / 90 = x / (Pi / 2), solve for x.Although you can find decimal approximations using a calculator, it is better to find these on the unit circle and start building your knowledge about radians and how they related to each other and the circle. You will soon find out that most of the time you are dealing with a 3, 4, 5 or right triangle.Turns out that here we are looking at the right triangle in the 4th quadrant of the unit circle. All angles in the 4th quadrant share certain principles. x is positive and y is negative in the 4th quadrant. This means that cos is going to be positive and sin and tan are going to be negative. All right triangles also have similar properties, their sin and cos are going to be equal or differ only by their sign and will be either Sqrt(2)/2 or -Sqrt(2)/2.Building this intuitive knowledge about the unit circle and the angles it contains will serve you much better than getting decimal approximations.sin( (7 [Pi])/4 ) = -1/Sqrt(2) = -Sqrt(2)/2cos( (7 [Pi])/4 ) = 1/Sqrt(2) = Sqrt(2)/2To find tangent, you need to do a little arithmetic. We know that tan(x) = sin(x) / cos(x), so,tan( (7 [Pi])/4 ) = sin( (7 [Pi])/4 ) / cos( (7 [Pi])/4 ) = (-Sqrt(2)/2)/(Sqrt(2)/2) = -1You can also remember that this is a right triangle and tangent is also going to be 1 or -1 depending on the quadrant.The cossec, sec and cot values are the reciprocals of these values:cossec( (7 [Pi])/4 ) = 1/sin( (7 [Pi])/4 ) = 1/(-Sqrt(2)/2) = -Sqrt(2)sec( (7 [Pi])/4 ) = 1/cos( (7 [Pi])/4 ) = 1/(Sqrt(2)/2) = Sqrt(2)cot( (7 [Pi])/4 ) = 1/tan( (7 [Pi])/4 ) = cos( (7 [Pi])/4 ) / sin( (7 [Pi])/4 ) = -1
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
What is the sin pi over 2?
sin(pi/2)=1
Y equals 4 sin x for x equals pi?
sin(pi) = 0 so 4*sin(pi) = 0 so Y = 0
What is sin of 3 pi over 2?
sin pi/2 =1 sin 3 pi/2 is negative 1 ( it is in 3rd quadrant where sin is negative
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 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?
sin(pi) = 0
What is the value of sin 3 pi over 2?
sin(3π/2) = -1
What are the exact values of the sine and cosine functions of 2pi over 65537?
sin(2*pi/65537) = 0.0001 cos(2*pi/65537) = 1.0000 to 4 dp.
