What does ine cosine and tangent mean?

Answer 1

Sine, Cosine and Tangent (abbreviated to sin, cos and tan) are three trigonometric ratios. They are used to find angles and sides in right angled triangles. There are more, but I will only explain these three.

In a right angled triangle, the hypotenuse (abbreviated to hyp) is ALWAYS opposite the right angle and is the longest side. The opposite (abbreviated to opp) is the side opposite to angle 'theta' (Θ, the unknown angle when finding angles). The adjacent (abbreviated to adj) is the side adjacent to (connecting) angle Θ and the right angle.

Here are the formulae:

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

The made up word 'SOH CAH TOA' can help. It is made from the first letters of 'Sine is Opposite over Hhypotenuse. and so on'.

You may also have heard of Inverse sin, cos and tan (written as sin-1, cos-1 and tan-1). You use these to find an angle. For example: if you are finding the sine of angle Θ, and the opposite is 40 and the hypotenuse is 68, 40/68 = 0.588235..., then, sin-1(0.588235...), so, Θ = 36.0 (to 3 significant figures).

If you have a scientific calculator, you can use the sin, cos and tan buttons to help work out sides and angles. Usually, pressing 2ndF or SHIFT then sin, cos or tan gives sin-1, cos-1 or tan-1.

To find sides of a right angled triangle using sin, cos or tan, you need an angle other than the right angle. Let's say you have a triangle in which opp is 40 cm and you want to find hyp. the angle is 45°. This is the process:

You have opp and you need to find hyp. Therefore we use sin = opp/hyp.

sin 40° = 40/hyp

40 * sin 40° = hyp

hyp = 25.7 (to 3 sig. fig.)

I hope I've kept this clear and I hope you now understand sine cosine and tangent well.