"Trigon" is greek for triangle, and "metric" is greek for measurement. The trigonometric ratios are special measurements of a right triangle (a triangle with one angle measuring 90o). Remember that the two sides of a right triangle which form the right angle are called the legs, and the third side (opposite the right angle) is called the hypotenuse.
There are three basic trigonometric ratios: sine, cosine, and tangent. Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non-90o angles.
Write expressions for the sine, cosine, and tangent of A.
The length of the leg opposite A is a. The length of the leg adjacent to A is b, and the length of the hypotenuse is c.
The sine of the angle is given by the ratio "opposite over hypotenuse". So,
The cosine is given by the ratio "adjacent over hypotenuse".
The tangent is given by the ratio "opposite over adjacent".
Generations of students have used the mnemonic "SOHCAHTOA" to remember which ratio is which. (Sine: Opposite over Hypotenuse, Cosine: Adjacent over Hypotenuse, Tangent: Opposite over Adjacent.)
Use the diagram shown. Find the sine, cosine, and the tangent of R and of S.
For the triangle shown, find sin G, cos G, and tan G.
Calculate the value of trigonometric ratio to the nearest ten thousandth.
Find the measure of the angle to the nearest degree.
Find the missing lengths in the diagram. Round all answers to the nearest hundredth. Check using the Pythagorean theorem.
Solve the triangle, giving the missing side lengths to the nearest tenth and all angles to the nearest degree.