Assuming that the angles are all stated in degrees: sin(45) = cos(45) = 1/2 sqrt(2) sin(45) cos(45) = (1/2)2 x (2) = 1/2 sin(230) = - 0.7660444 sin(45) cos(45) - sin(230) = 0.5 + 0.7660444 = 1.2660444 (rounded)
sin(x) + cos(x) = sqrt(2) · sin(45°+x)
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 = c2a2 + a2 = 122a2 = 1a2 = 1/2a = √(1/2)a = 1/√(2) * (√(2)/√(2))a = √(2) / 2Since sin is defined as opp/hyp, sin 45 degrees (pi/4 radians) = (√(2)/2)/1 = √(2)/2I 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).
0.34202014332566873304409961468226
1.570796327
If tan 3a is equal to sin cos 45 plus sin 30, then the value of a = 0.4.
Assuming that the angles are all stated in degrees: sin(45) = cos(45) = 1/2 sqrt(2) sin(45) cos(45) = (1/2)2 x (2) = 1/2 sin(230) = - 0.7660444 sin(45) cos(45) - sin(230) = 0.5 + 0.7660444 = 1.2660444 (rounded)
6.25
to find sin 35 here we take the angle = x=15 then 3x=45 , 4x=60 then 4x-3x=60-45 then by putting sin on rhs we will get cos 35 and sin 35 hope it helped you
= 1/sqrt(2) = 0.7071
what is the value of sin 75 degree
0.96593 (rounded)
sin(75) = sin(45 + 30) = sin(45)*cos(30) + cos(45)*sin(30) = [1/sqrt(2)]*[sqrt(3)/2] + [1/sqrt(2)]*[1/2] = 1/[2*sqrt(2)]*[sqrt(3) + 1] that is [sqrt(3) + 1] / [2*sqrt(2)]
sin-1(0.707) = 44.99134834 or about 45 degrees
sin 300 = -sin 60 = -sqrt(3)/2 you can get this because using the unit circle.
cos(45) = sin(45) You can see this as follows: imagine a circle with radius 1. The point on the circle with angle 45 degrees, lies on the line y=x, equally far from the x-axis (cos) as the y-axis (sin). The angle for both must be 45, because x and y are orthogonal: 90 deg, so if the angle with x is 45, then the angle with y must be 90-45=45. So: for this point, both angles are 45, and the distance to x (cos) is equal to the distance to y (sin). Therefore, cos(45) = sin(45). Additionally, cos(45) = sin(45+90) = sin(45+360n) = sin(135+360n) with n integer.
sin theta = opp/hyp sin 45 = opp/1 opp = sin 45 = sqrt(2)/2 ~= 0.7071