Math: Trigonometry

unit circle

A unit circle is a circle with a radius of 1 that is useful in trigonometry. Angles are measured starting from the positive x-axis in quadrant 1 and continuing counterclockwise. For the ACT, you should definitely know the radian measures of the axes and in which quadrants the trig functions are positive or negative. Important to know! The mnemonic All Students Take Calculus can help you remember where functions are positive: Q1: all, Q2: sine, Q3: tangent, Q4: cosine.

SOHCAHTOA

SOHCAHTOA is a mnemonic that helps us remember how to compute the sine, cosine and tangent of an angle in a right triangle. Sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent.

reciprocal identities

Secant theta(sec) = 1/cos theta. Cosecant theta (csc) = 1/sin theta. Cotangent theta (cot) = 1/tan theta.

pythagorean identity

The Pythagorean Identity is sin^2(theta) + cos^2(theta) = 1.

Law of sines

The law of sines is: sinA/a = sinB/b = sinC/c

converting degrees to radians

To convert degrees to radians, multiply by rt/ 180. Example: Convert 270° to radians. 270 xpi / 180 = Зpi/2

converting radians to degrees

To convert radians to degrees, multiply by 180/pi. Example: Convert 3pi/2 to degrees. 3pi/2 * 180/pi = 270°.

inverse trig functions

inverse trig functions are used to obtain an angle measure from any of the angle's trigonometric ratios. Written, for example, as sin^-1(1/2) = theta or arctan 2/3 = theta Example: What is arcsin(1/2)? (The ACT will give you a table of values or a diagram to solve this, or you can use your calculator) Answer: 30°