Trigonometry Boards for School Maths Lab

Quick Answer: Trigonometry Boards are maths lab boards for teaching the trigonometric ratios, usually built around a unit circle with a rotating radius arm so that sine and cosine can be read as lengths. Classes use a trigonometry board to extend sin, cos and tan beyond 90°, find their signs in the four quadrants and connect the circle to the wave graphs.

From Right Triangles to a Rotating Radius

Right-triangle trigonometry stops at 90°, but the trigonometric functions do not. A board of the usual unit-circle design fixes a circle of radius one unit on x and y axes and lets a radius turn from the positive x-axis. For any angle, the foot of the perpendicular from the tip gives the cosine as the horizontal distance and the sine as the vertical distance.

Turning the arm through the quadrants shows the signs without a rule to memorise: in the first quadrant sine and cosine are both positive, in the second only sine is positive, in the third only tangent and in the fourth only cosine. Special angles such as 30°, 45° and 60° can be checked against their exact values, and the identity sin²θ + cos²θ = 1 is simply Pythagoras applied to the radius.

Recording the height of the tip every 15° and plotting it against the angle produces the sine curve, which makes the link between circular motion and periodic graphs concrete for students who have only seen the graph drawn from a table.

Specifications

Applications

• Reading the sine and cosine of any angle as the coordinates of the tip of the radius
• Finding the sign of each ratio in each quadrant (the All, Sin, Tan, Cos pattern)
• Checking exact values for 30°, 45°, 60° and 90° against the board
• Plotting tip heights against angle to draw the sine and cosine graphs

Care & Handling

• Turn the radius arm of the trigonometry board gently in either direction and do not force it past any stop.
• Clean the markings with a dry or slightly damp cloth, avoiding solvents that could lift printed scales.
• Store the boards flat or upright in a rack so they do not bow.

Why Choose LabEquip

Senior secondary teachers use these boards when students can handle right-triangle ratios but struggle with angles beyond 90° and with negative values. They belong to LabEquip’s Mathematics School Lab Products range, and the Theodolite Model there supplies the practical heights-and-distances side of the same topic. Ask about board details on the contact page.

Frequently Asked Questions

Why are sine and cosine defined on a unit circle?

With a radius of 1, the hypotenuse of every triangle formed has length 1, so cosine equals the x-coordinate and sine equals the y-coordinate of the point on the circle. This definition works for any angle, including angles greater than 90 degrees and negative angles.

How do you remember the signs of trig ratios in each quadrant?

Many students use All, Sin, Tan, Cos, going anticlockwise from the first quadrant: all ratios positive, then only sine, then only tangent, then only cosine. On the board the signs follow directly from whether the x and y coordinates are positive or negative.

Where is tangent shown on a trigonometry board?

Tangent equals sine divided by cosine, which is the gradient of the radius. On boards with a tangent line drawn at x equals 1, the extended radius meets that line at a height equal to tan θ, which shows why tangent grows without limit near 90 degrees.

How does the board explain sin²θ + cos²θ = 1?

The horizontal distance, the vertical distance and the radius form a right triangle with hypotenuse 1. By Pythagoras, cos²θ plus sin²θ equals 1 squared, which is 1, for every angle.

How is the sine graph drawn from the board?

Turn the radius in steps, for example every 15 degrees, and record the height of its tip. Plot each height against the angle from 0 to 360 degrees and join the points. The result is one full wave of the sine curve; the horizontal distances give the cosine curve.

Is sin 150° the same as sin 30°?

Yes. The radius at 150 degrees is the mirror image of the radius at 30 degrees in the y-axis, so its tip is at the same height and both sines equal one half. Their cosines have opposite signs.

Last Updated: September 2026