The sine of one angle = the cosine of the other angle. The cosine of one angle = the sine of the other angle. If you understand SOH-CAH-TOA and right triangles, this is logical: From SOH and CAH, you can see that the only difference between the sine and the cosine is that the sine has the Opposite side length in the numerator and the cosine has
1) Draw a right triangle and label one of the (non 90∘ 90 ∘) angles α α. 2) You know that the tangent of α α is 1 2 1 2. Since tan = opposite adjacent tan = opposite adjacent, you can label the side of the triangle adjacent to α α "1" and the opposite side "2". 3) By the Pythagorean theorem, you can find the length of the hypotenuse
Any triangle whose sides are in the ratio 3:4:5 is a right triangle. Such triangles that have their sides in the ratio of whole numbers are called Pythagorean Triples. There are an infinite number of them, and this is just the smallest. cscθ = 1 sinθ = 5 3. cosθ = AB AC = 4 5. secθ = 1 cosθ = 5 4. tanθ = BC AB = 3 4. cotθ = 1 tanθ = 4 3.Sin, Cos, and Tan are the basic trigonometric functions considered while solving trigonometric problems. Sin, Cos, and Tan are abbreviated for sine, cosine, and tangent, respectively. These mathematical functions are used to study the relationship between the angles and sides of a triangle. What about tan? Well, tan = sin/cos, so we can calculate it like this: tan(30°) = sin(30°)cos(30°) = 1/2√3/2 = 1√3 = √33 * tan(45°) = sin(45°)cos(45°) = √2/2√2/2 = 1 . tan(60°) = sin(60°)cos(60°) = √3/21/2 = √3 * Note: writing 1√3 may cost you marks so use √33 instead (see Rational Denominators to learn more). Quick You can see that tan(x) is very different to cos(x) and sin(x). tan(x) is very much what the name implies, it is a result of the y component of a point rotating around the unit circle tracing out
The range is from −1 to +1 since this is an abscissa of a point on a unit circle. Function y = tan(x) is defined as sin(x) cos(x). The domain of this function is all real numbers except those where cos(x) = 0, that is all angles except those that correspond to points (0,1) and (0, − 1). These angles where y = tan(x) is undefined are π 2