How To Use A Calculator For Trigonometry

Since trigonometry is a branch of math that involves finding the functions of angles, it's important to understand how to use a scientific calculator. It's particularly essential if you plan to have a career in which you'll use real-life applications of trigonometry, such as architecture, engineering, and manufacturing. A basic calculator just won't do because, with all types of trigonometry, you need specific function buttons — sine, cosine, and tangent — on a scientific calculator to complete trigonometric ratios.

First things first, make sure that your calculator is set to solve the functions in degrees. Some calculators don't show anything on the screen when degrees are selected, while others will have "Deg" or "R" in one of the corners. If the calculator is not set to degrees, then you may see "Rad" or "R" — which you would use when dealing with angle measurements in a circle — in one of the corners. You can change it by pressing the "Deg" or "Rad" buttons on the calculator. Otherwise, you may need to review the manual to find the right combination of buttons to press.

For trigonometry involving a right triangle, you can use the "sin," "cos," and "tan" buttons on a scientific calculator to determine the trigonometric functions of an acute angle — the formula for which is determined using the triangle's hypotenuse, adjacent, and opposite sides. Let's say that you have a right triangle with a 46-degree acute angle and an adjacent side value of 23, and you need to find the opposite side value. On some calculators, you can enter "23 x 46tan" (or vice versa) and press the equals button for a result of 23.82. If your calculator allows you to type out the full formula, you can input "23 x tan(46)", closing the parentheses and pressing equals for the same result.

You can also use a scientific calculator to find reciprocal values with the cosecant, secant, and cotangent buttons — which are generally labeled "csc," "sec," and "cot" (respectively). However, these functions don't always have dedicated buttons, in which case you will need to input the reciprocal manually. Let's say that you have a right triangle with a 32-degree acute angle and opposite side value of 12, and you need to find the hypotenuse. Some calculators require you to enter "12 ÷ 32sin," while others take the full equation "12 ÷ sin(32)" — closing the parentheses and pressing equals as necessary — to get 22.64.

To find the measure of an acute angle using the trigonometric ratios of a right triangle, you need to use an inverse function, such as arcsin, arccosine, or arctangent. Most of the time, a scientific calculator will have a "-1" above the respective buttons to represent them. It's usually written in a different color to make it stand out and means that you have to press the "2nd" button first to access those "secondary" functions. Let's say that you have a right triangle with a hypotenuse value of 21 and an adjacent value of 11. So, to find the measure of the acute angle, you need to enter "(11 ÷ 21)'2nd'cos^-1" or "'2nd'cos^-1(11 ÷ 21)," depending on the type of calculator you have, to get 58.41 degrees.

However, the button to access secondary functions could be labeled as "Shift" or even look like two arrows pointing away from each other, such as on Samsung's default mobile phone calculator app. In some cases, though, the button to access the secondary functions remains on until you press it again. You might need to play around with the buttons or review the manual to learn how it works.