Trigonometric identities are equations that involve trigonometric functions and are true for all possible values of the variables. These identities play a key role in simplifying expressions and solving trigonometric equations. Here are some commonly used identities:
These identities are derived from the Pythagorean theorem and hold true for all angles.
Special angle relationships refer to the angles that result in specific trigonometric ratios. The two most commonly encountered special angle relationships are the 30°-60°-90° and 45°-45°-90° triangles.
In a 30°-60°-90° triangle, the sides are in the ratio of 1:√3:2. For example, if the shortest side (opposite the 30° angle) is 5, the other two sides would be 5√3 and 10, respectively.
In a 45°-45°-90° triangle, the sides are in the ratio of 1:1:√2. If one side has a length of 4, the other two sides would also have a length of 4.
Remember, mastering trigonometric identities and special angle relationships will greatly simplify your trigonometric calculations and problem-solving abilities!