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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.
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∙ 12y ago
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How does the tangent function relate to sine and cosine?
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
Do you need a right traingle to use sine cosine and tangent?
Yes, sine, cosine, tangent definitions are based on right triangles
Does tangent of x equal cosine divided by sine?
No, it does not.
What jobs use sine cosine and tangent?
Trigonometry
What do sin and cos mean in math?
sin stands for sine cos stands for cosine and tan stands for tangent
How does the tangent function relate to sine and cosine?
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
How do you find sine cosine and tangent of 210 degrees?
Sine = -0.5 Cosine = -0.866 Tangent = 0.577
Do you need a right traingle to use sine cosine and tangent?
Yes, sine, cosine, tangent definitions are based on right triangles
What is the relationship between the tan and cot?
Cotangent is 1 / tangent. Since tangent is sine / cosine, cotangent is cosine / sine.
The laws of sine cosine and tangent are used where?
in trigonometry
Does tangent of x equal cosine divided by sine?
No, it does not.
What jobs use sine cosine and tangent?
Trigonometry
What does tangent on a scientific calculator mean?
It is a trigonometric function, equivalent to the sine of an angle divided by the cosine of the same angle.
What do sin and cos mean in math?
sin stands for sine cos stands for cosine and tan stands for tangent
If the tangent of an angle is 2 what is the cosine?
The cosine is ±1/sqrt(5) = ±0.4472 (approx).
How do you find 2 missing sides of a right triangle?
Two methods to try . #1 Use pythagoras h^ = a^2 + a^2 NB THis is only good if you know that the two unknown sides are the same length. #2 Use trigonometry (trig.) This is good if you know the hypotenuse and one of the angles. Sine(angle) = opposite/ hypotenuse Hence opposite side = hypotenuse X sine(angle) Similarly Cosine(angle) = adjacent / hypotenuse. adjacent side = hypotenuse X Cosine(angle) Here is an example If you known the hypotenuse is a length of '6' and the angle is 30 degrees. Then opposite = 6 X Sin(30) opposite = 6 x 0.5 = 3 So the length of the oppisute sides is '3' units. NB DO NOT make the mistakes of saying Sin(6 X 30) = Sin(180) Nor 6 x 30 , nor Sin(6) X 30 , nor any other combination. You MUST find the SINE of the angle , then multiply it to the given length. Similarly for Cosine and Tangent.
The tangent of an angle equals the ratio of the?
Sine of the angle to its cosine.
