Trigonometry Worksheets – New & Engaging

How Do You Do SOH CAH TOA?

The image below shows the rules for finding the angle or opposite side using sine (pronounced 'sign') equals opposite side divided by the hypotenuse. In the trigonometry example below the opposite side measures 3.5 cm.

The image below shows the formula for finding the adjacent side, the hypotenuse or the missing angle. The rule states that cosine equals the adjacent side divide by hypotenuse. What is the hypotenuse? Pythagoras Worksheets. The adjacent side below is 4 cm.

The image below shows the rule for the tangent ratio, opposide side divide by adjacent side. The missing opposite side in the trigonometry example below is 10.7 cm.

What Are The 3 Trigonometric Ratios?

The image below shows the graph of y = sin (x). It has a maximum value of 1 and minimum value of -1. The graph meets the x axis at 180º and 360º. y = sin x repeats every 360º.

The cosine graph repeats itself every 360º (2π radians). The cosine of an angle (x) is the ratio of the adjacent to the hypotenuse.

The graph of y = tan (x) has vertical asymptotes at 90º, 270º and every 180º repetitions. It is useful to remember that tan Θ = sin Θ  / cos Θ .

Special Right Triangles

Special right triangles are useful for quickly remembering important trigonometric ratios such as sin30°, cos30° and tan30°, sin60°, cos60° and tan60°, sin45°, cos45° and tan45°.

What Is The Cosine Rule?

The cosine rule states that a² = b² + c² - 2bc cosA. If angle C equals 60º for example then side c is the corresponding angle which could equal 15 cm for example.

The Sine Rule

The sine rule states that a / sin A = b / sin B = c / sin C. It is also true for the inverse ratios.

Area of a Triangle

When the area of a triangle has a perpendicular height the formula for area is half base multiplied by height. When the perpendicular height is not given then we can use trigonometry. The formula is shown below, it states that ½ ab sin C = area of any triangle.

Trigonometry Question 1

Find the length of the hypotenuse giving your answer correct to 2 decimal places. The hypotenuse is the longest side of the triangle. Use SOHCAHTOA, the answer is 9.45 cm.

Trigonometry Question 2

Find the size of the angle marked x. Give the answer correct to 2 decimal places. This question involves rounding. It's important not to round too early in the solution. We first use pythagoras theorem to find the diagonal of the square cross-section. The diagonal measures 16.97056... Next we use the inverse of tangent ratio, arctan (tan^-1 x) to find the missing angle x. The angle is 35.26º.