What do you call sin cos and tan?
Introduction: In this lesson, three trigonometric ratios (sine, cosine, and tangent) will be defined and applied. These involve ratios of the lengths of the sides in a right triangle. In a right triangle, one angle is 90º and the side across from this angle is called the hypotenuse.
The 6 Trig Ratios. For any right triangle, there are six trig ratios: Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Here are the formulas for these six trig ratios: Given a triangle, you should be able to identify all 6 ratios for all the angles (except the right angle).
- The tangent ratio is a tool used with right triangles that allows one to find the length of the sides of a triangle given the degree of its angles. It can also be used to find the degrees of its angle given the length of two of its sides.
- There are three steps:
- Choose which trig ratio to use. - Choose either sin, cos, or tan by determining which side you know and which side you are looking for.
- Step 1: Choose which trig ratio to use.
- Step 2: Substitute.
- Step 3: Solve.
- Step 1: Choose the trig ratio to use.
- Step 2: Substitute.
- The hypotenuse in a right triangle is always larger than the adjacent side, so for angles greater than zero but less than 90º the cosine ratio will be less than 1. For angles outside of these limits, the sine ratio can have values from -1 to 1.
The functions of sin, cos and tan can be calculated as follows: Sine Function: sin(θ) = Opposite / Hypotenuse. Cosine Function: cos(θ) = Adjacent / Hypotenuse. Tangent Function: tan(θ) = Opposite / Adjacent.
- In a right triangle ABC, whose right angle is A, the tangent ratio of the angle B is the opposite leg over the adjacent leg. Therefore, in a right angle triangle, the tangent ratio of an angle, except the right angle, is: tan = sin / cos .
- For any right triangle, there are six trig ratios: Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
- The Sine Rule. The Law of Sines (sine rule) is an important rule relating the sides and angles of any triangle (it doesn't have to be right-angled!): If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle, then: a = b = c. sinA sinB sinC.
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 .
- 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 .
- The cofunction identities are as follows: These identities show how the function values of the complementary angles in a right triangle are related. For example, cosθ = sin (90° – θ) means that if θ is equal to 25 degrees, then cos 25° = sin (90° – 25°) = sin 65°.
- The graphs of functions defined by y = sin x are called sine waves or sinusoidal waves. Notice that the graph repeats itself as it moves along the x-axis. The cycles of this regular repeating are called periods. This graph repeats every 6.28 units or 2 pi radians.
Updated: 18th November 2019