What is the difference between the sine and cosine function?
Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .
What is similar and different about the sine and cosine functions?
The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.
Why do we use sine?
The sine function is defined as the ratio of the side of the triangle opposite the angle divided by the hypotenuse. This ratio can be used to solve problems involving distance or height, or if you need to know an angle measure. To find the length of the side opposite the angle, d, we use the sine function.
What is the full name of sin?
Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
How is the sine related to the cosine?
The relationship between the cosine and sine graphs is that the cosine is the same as the sine – only it’s shifted to the left by 90 degrees, or π /2. The trigonometry equation that represents this relationship is Look at the graphs of the sine and cosine functions on the same coordinate axes, as shown in the following figure.
How do you write a sine function?
To write the sine function in terms of cotangent, follow these steps: Start with the ratio identity involving sine, cosine, and tangent, and multiply each side by cosine to get the sine alone on the left. Replace cosine with its reciprocal function. Solve the Pythagorean identity tan 2θ + 1 = sec 2θ for secant.
Is cotangent sine over cosine?
Cotangent we can write as cosine over sine , so notice those two are reciprocals, tangent and cotangent are reciprocals. Secant is the reciprocal of cosine, and cosecant is the reciprocal of sine. Notice that people get confused sometimes because they think the s and the s should go together, the c and the c should go together, they don’t.
What does the sine function represent?
Answer Wiki. Sine function represents the vertical position of a point on a spinning circle. Therefore, it can be used to model periodic behaviour.