0
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.
Still curious? Ask our experts.
Chat with our AI personalities
Devin
Beau
ViviAdd your answer:
Earn +20 pts
What is sin 45?
one over the square root of 2 or 0.850903525
What is sin 45 degrees?
1/square root 2
What if the sine of an angle is 0.707 what is value of that angle in degrees?
sin-1(0.707) = 44.99134834 or about 45 degrees
When is the shadow equal in length to your height?
When the angle of elevation equals 45 degrees. tan-1(1) = 45 degrees.
What is the cos of a 45 degree angle?
cos 45o = 1/√2 = 1/2 x √2 ≈ 0.707
X is acute and sin x equals cos x Find cos?
x = 45 degrees sin(x) = cos(x) = 1/2 sqrt(2)
Fill in the blank Cos equals Sin 45?
45
Find out value of sin 45 cos 45 - sin 230?
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)
How do you solve sin x plus cos x equals zero?
The statement of the problem is equivalent to sin x = - cos x. This is true for x = 135 degrees and x = -45 degrees, and also for (135 + 180n) degrees, where n is any integer.
What is the cot of a 45 degree angle?
1 cot(theta)=cos(theta)/sin(theta) cos(45 degrees)=sqrt(2)/2 AND sin(45 degrees)=sqrt(2)/2 cot(45 deg)=cos(45 deg)/sin(deg)=(sqrt(2)/2)/(sqrt(2)/2)=1
Why does cos negative theta equals positive theta?
You must think of the unit circle. negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example: cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4
Sin x plus cos x?
sin(x) + cos(x) = sqrt(2) · sin(45°+x)
Find the value of a if tan 3a is equal to sin cos 45 plus sin 30?
If tan 3a is equal to sin cos 45 plus sin 30, then the value of a = 0.4.
What is six trigonometric ratios of 45 degrees?
sin(45) = cos(45) = 1/sqrt(2) tan(45) = cot(45)= 1 csc(45) = sec(45) = sqrt(2)
Is the cosine sine and tangent of an angle equal to each other?
No; those could be three different values, or sometimes two of them might be the same. For example, if the angle is 45 degrees, the values are about... cos:0.707 sin: 0.707 tan: 1 For 45 degrees, the cosine and sine are the same. For 36 degrees, cos:0.809 sin: 0.588 tan: .727
What is cos 45?
square root 2 divided by 2 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), because the angle is 45 for both (because x and y are orthogonal: 90 deg). We have cos^2 + sin^2 = 1 . But from the above we know that cos(45) must be equal to sin(45), because they represent the distances to x and y axis respectively, and the point is exactly inbetween, so the distances are equal. We get cos^2 + sin^2 = cos^2 + cos^2 = 2cos^2 = 1 cos = 1/sqrt(2) = sqrt(2) / 2
Cos 195 degree use the trigonometry functions of quadrantal angles and special to find the exact value?
cos(195) = cos(180 + 15) = cos(180)*cos(15) - sin(180)*sin(15) = -1*cos(15) - 0*sim(15) = -cos(15) = -cos(60 - 45) = -[cos(60)*cos(45) + sin(60)*sin(45)] = -(1/2)*sqrt(2)/2 - sqrt(3)/2*sqrt(2)/2 = - 1/4*sqrt(2)*(1 + sqrt3) or -1/4*[sqrt(2) + sqrt(6)]
