Back to Index to Your Calculator
You can work with angles in degrees, radians or gradients. The default setting is degrees, and this is shown by a very tiny D in the top line of the display. If you are working in degrees you can use degrees and decimal degrees or degrees, minutes and seconds - see the Page on sexagesimal.
Radians are described on the Page on Circles. To use radians (or gradients) you use SETUP (press SHIFT first of course) and then select option 4 (or 5). R (or G) will appear in the top line of the display. To convert back to degrees use SETUP and select 3.
If you normally work in degrees do remember to switch back to degrees after you have used radians!
When you are in degrees mode you normally enter angles in degrees, and answers will always be in degrees (and of course similarly for radians or gradients), but you can always enter angles as degrees, radians or gradients, whatever setting you are using, by using the DRG key (over Ans so use the SHIFT key of course). This allows you to choose 1 for degrees, 2 for radians or 3 for gradients (these numbers appear in the display when you press DRG). To enter an angle as 0.5 radians when you are in degree mode you would enter 0.5 DRG 2 = and get the answer 28.65° (to two decimal places).
Gradients are discussed on their own Page. Today the slope of a line is usually defined as 
, the ratio of the change in y to the change in x, that is, the tangent of the angle, and given as a decimal number, for example 0.7 or -1.3. A vertical line, for example a cliff, is said to have an infinite slope, positive if you are climbing up it and negative if you are jumping off it. For nearly four thousand years, from the digging of the first irrigation channels in Ancient Mesopotamia to the construction of the railways in the 19th century CE, the gradient has been the ratio of the vertical height gained to the distance along the slope, that is, the sine of the angle, and was given as a unit fraction such as one in five, although today they are usually given as a percentage, for example on road signs warning you about steep hills. You might find it interesting to switch to radians mode then enter 100 SHIFT DRG 3 =
To find the sine of an angle you use the sin key. Pressing it opens the brackets, but you should always close them yourself. If you do not close them some calculators will flag a syntax error but others will close them for you - this is dangerous because it may lead to a closing bracket being put in in the wrong place. This is discussed in greater detail here. Try finding sin 55°. You use the cos and tan keys in exactly the same way. Remember that trigonometrical functions will almost always produce an irrational answer so your calculator will give it to ten figures - irrational numbers are discussed on the Natural Numbers Page. The answer is stored in Ans to full accuracy if you need to use it in other calculations, but you will almost certainly lose marks in an exam if you write the answer down without rounding it sensibly. This is discussed, with some worked examples, on the Page on the Using Memories.
Sines and cosines are always in the range -1 to +1, and if you try to find tan 90° you will get a maths error.
When we are using the inverse trigonometrical functions, sin-1 etc we need to remember that although for each value of θ there is just one value of sin θ, one value of cos θ and one value of tan θ, for each value of sin-1 θ cos-1 θ and tan-1 θ there are two values of θ, in different quadrants (more than two if you consider angles of less than 0° or more than 360°), but your calculator will only give you one. This is particularly important when using the Sine Rule.
Hyperbolic functions are used in a similar way to trigonometrical functions. First you press the hyp key: this gives you a list of options, 1 for sinh etc. Choose the function you want, for example 1. Then enter the value and close the brackets. Check that you have understood these simple instructions by trying to find the value of tanh-1 0.84 which should be 1.22 to two decimal places.
