Trigonometry is where the TI-84 earns its keep for most high school students. From evaluating trig functions to graphing complete sine waves, from solving triangles to analyzing periodic behavior, the calculator streamlines calculations that would otherwise require extensive reference tables or prolonged hand computation.
Introduction
Trigonometry is where the TI-84 earns its keep for most high school students. From evaluating trig functions to graphing complete sine waves, from solving triangles to analyzing periodic behavior, the calculator streamlines calculations that would otherwise require extensive reference tables or prolonged hand computation.
This guide covers every trig-related feature the TI-84 offers: the critical Degree/Radian mode setting, evaluating the six trigonometric functions, working with inverse trig functions, graphing sinusoidal functions with amplitude and period transformations, and using the ANGLE menu for coordinate conversions and degree-minute-second notation. Each section includes worked examples and the most common mistakes to avoid.
Trig mode errors are among the most frequent calculator mistakes at every level from high school through college. A student who computes sin(30) expecting 0.5 but gets -0.988 due to a Radian mode setting has made an error that will produce wrong answers throughout an entire homework assignment or exam section. Understanding and managing the mode setting is the single most important skill in TI-84 trigonometry.
Degree vs. Radian Mode: The Critical Setting
Press MODE and look for the row containing RADIAN and DEGREE. This single setting determines how all trigonometric functions interpret angle inputs and produce angle outputs. Selecting RADIAN means all angles are in radians (where 2*pi radians = 360 degrees). Selecting DEGREE means all angles are in degrees.
Use Degree mode for: high school geometry and trigonometry courses that work with degree angles, SAT and ACT problems (almost always use degrees), AP Statistics (no trig involved), and any problem where angles are given as whole-number or simple decimal degree values.
Use Radian mode for: pre-calculus courses covering unit circle, calculus (derivatives and integrals of trig functions require radians), AP Calculus (the exam expects radian measure), and any problem where angles are expressed as multiples or fractions of pi. When in doubt about which mode a problem requires, look for clues in how angles are expressed: if you see "45°" use Degree mode; if you see "pi/4" use Radian mode.
Basic Trig Functions
The SIN, COS, and TAN keys are in the middle-left section of the keypad. Enter trig expressions by pressing the function key, typing the angle, and closing the parenthesis before pressing ENTER. Always include the closing parenthesis: sin(30) computes correctly, while sin(30 without the closing parenthesis may give an unexpected result depending on what follows it in the expression.
In Degree mode: sin(30) returns 0.5, cos(60) returns 0.5, tan(45) returns 1. In Radian mode: sin(pi/6) returns 0.5, cos(pi/3) returns 0.5, tan(pi/4) returns 1. The same mathematical values, but the input format differs based on mode.
The calculator has three additional trig functions accessible through the catalog: csc( (cosecant = 1/sin), sec( (secant = 1/cos), and cot( (cotangent = 1/tan). These are not on the main keypad but are available in CATALOG (2ND+0). Alternatively, compute them using their reciprocal definitions: type 1/sin(X) to compute csc(X) without needing the csc( function specifically.
Inverse Trig Functions
Access inverse trig functions using the 2ND key followed by the trig key: 2ND+SIN gives arcsin (sin inverse), 2ND+COS gives arccos, and 2ND+TAN gives arctan. These functions find the angle whose trig value you specify.
In Degree mode, arcsin(0.5) returns 30, confirming that the angle with a sine of 0.5 is 30 degrees. arccos(0.5) returns 60. arctan(1) returns 45. In Radian mode, the same calculations return pi/6 (approximately 0.5236), pi/3 (approximately 1.0472), and pi/4 (approximately 0.7854).
The domain restrictions of inverse trig functions are important: arcsin returns values in [-90°, 90°] (or [-pi/2, pi/2] in radians), arccos returns values in [0°, 180°] (or [0, pi]), and arctan returns values in (-90°, 90°) (or (-pi/2, pi/2)). These restrictions mean the calculator returns only the principal value. For a triangle problem where you know the opposite side is 7 and the hypotenuse is 10, arcsin(7/10) correctly gives approximately 44.4° — the acute angle. If you need an obtuse angle, compute 180 minus the arcsin result.
Graphing Trig Functions
Press Y= and enter a trig function using X as the angle variable. For clean graphing, press ZOOM → 7:ZTrig first — this sets an appropriate window with X ranging from approximately -6.28 to 6.28 (two periods of a standard sine wave) and Y from -4 to 4. In Degree mode, ZTrig sets X from -360 to 360.
Explore amplitude, period, and phase shift transformations: Y1 = sin(X) plots the basic sine wave with amplitude 1 and period 2*pi. Y1 = 2*sin(X) doubles the amplitude to 2. Y1 = sin(2X) halves the period to pi (the graph completes two full cycles in the ZTrig window). Y1 = sin(X - pi/4) shifts the graph right by pi/4 radians. Y1 = sin(X) + 1 shifts the graph up one unit.
Use TRACE after graphing to identify key features: peaks where the sine reaches its maximum of 1 (at X = pi/2, 5*pi/2, etc.), troughs at the minimum of -1 (at X = 3*pi/2, 7*pi/2, etc.), and zero crossings at X = 0, pi, 2*pi, etc. For transformed functions, the amplitude, period, phase shift, and vertical translation all change these key point locations, and TRACE provides a direct way to verify your analytical predictions.
The ANGLE Menu
Press 2ND+APPS to access the ANGLE menu. This menu provides angle-unit conversion tools and coordinate system conversion functions that complement the main trig capabilities.
The degree symbol (option 1) forces an angle to be interpreted as degrees regardless of current MODE. For example, in Radian mode, typing sin(30°) using the degree symbol from the ANGLE menu returns 0.5 (the sine of 30 degrees) instead of sin(30 radians). This is useful when you are working in radian mode for most of a problem but encounter a specific angle given in degrees.
The DMS conversion (option 4, labeled as ▶DMS) converts decimal degrees to degrees-minutes-seconds format. For example, 44.4° in decimal form is approximately 44° 24' 0" in DMS format. The polar-rectangular conversion functions R▶Pr, R▶Pθ, P▶Rx, and P▶Ry convert between (x,y) rectangular coordinates and (r,θ) polar coordinates directly, which is useful for problems involving vectors, complex numbers in polar form, and parametric equations.