The Right Triangle Right Triangle Pythagorean Theorem Trigonometric Functions Inverse Trig Functions Trigonometric Expressions

Right Triangle

Key Point: In any right triangle: (1) the sum of the acute angles equals 90°(2) the hypotenuse is the side of greatest length(3) the greater side lies opposite the greater angle.

Pythagorean Theorem

Key Point: The Pythagorean theorem states:

in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

c2 = a2 + b2

Trigonometric FunctionsThree trigonometric ratios, called functions, are the sine, cosine, and tangent. The sine function expresses the ratio of the length of the opposite side to the hypotenuse. The cosine function expresses the ratio of the length of the adjacent side to the hypotenuse. The tangent function expresses the ratio of the length of the opposite side to the adjacent side.

Inverse Trig Functions

Key Point: Inverse trig functions are used to find the ratio of sides when the angle is known. Three inverse trig functions are arcsin, arccos, and arctan. They are usually written sin-1, cos -1, and tan -1.

sin-1 0.74314 = 48.0o

cos-1 0.74314 = 42.0o

tan-1 0.74314 = 36.6o

Trigonometric Expressions

Key Point: When rearranging the equations of the functions to solve for an unknown side or angle, sin θ (or cos θ or tan θ) is one quantity and cannot be separated.