Investigatory Project
Lesson 1: Trigonometric Functions of an Acute Angle c a b
C
A
B
The ratios of the lengths of the sides of a right triangle are called the trigonometric ratios. For convenience, we will name the three sides and three vertices of the right triangle as, a, b, and c for sides and the A, B, and C for the vertices as shown in the figure:
Sine (sin) Function of an acute angle of a right triangle is equal to the ratio of the length of the opposite leg to the length of the hypotenuse.
Cosine (cos) Function of an acute angle of a right triangle is equal to the ratio of the length of the adjacent leg to the length of the hypotenuse.
Tangent (tan) Function is equal to the ratio of the length of the opposite leg to the length of the adjacent leg.
The reciprocal of the sine function is the Cosecant (csc) Function. The reciprocal of cosine and tangent are Secant (sec) and Cotangent (cot) function respectively.
Right-Triangle-Based Definitions of Trigonometric Functions of angle A * sin A=ac * cos A=bc * tan A=ab * csc A=ca * sec A=cb * cot A=ba
Right-Triangle-based definitions of Trigonometric Functions of angle B * sin B=bc * cos B=ac * tan B=ba * csc B=cb * sec B=ca * cot B=ab
Lesson 2: Right Triangle If this is the angle under consideration. h This side is called the opposite side because it is opposite the angle.
This side is called adjacent side because it is near the angle. θ A triangle in which one angle is a right angle is called a right triangle. In a right triangle, the three sides are given special names. a. The hypotenuse, which is the longest side, is the side opposite the 90° angle; and b. The remaining two sides are called the legs of the triangle. The two other sides are named in relation to another known angle (or unknown angle under consideration).
Lesson 3: Solution to Right Triangles
To solve
C
A
B
The ratios of the lengths of the sides of a right triangle are called the trigonometric ratios. For convenience, we will name the three sides and three vertices of the right triangle as, a, b, and c for sides and the A, B, and C for the vertices as shown in the figure:
Sine (sin) Function of an acute angle of a right triangle is equal to the ratio of the length of the opposite leg to the length of the hypotenuse.
Cosine (cos) Function of an acute angle of a right triangle is equal to the ratio of the length of the adjacent leg to the length of the hypotenuse.
Tangent (tan) Function is equal to the ratio of the length of the opposite leg to the length of the adjacent leg.
The reciprocal of the sine function is the Cosecant (csc) Function. The reciprocal of cosine and tangent are Secant (sec) and Cotangent (cot) function respectively.
Right-Triangle-Based Definitions of Trigonometric Functions of angle A * sin A=ac * cos A=bc * tan A=ab * csc A=ca * sec A=cb * cot A=ba
Right-Triangle-based definitions of Trigonometric Functions of angle B * sin B=bc * cos B=ac * tan B=ba * csc B=cb * sec B=ca * cot B=ab
Lesson 2: Right Triangle If this is the angle under consideration. h This side is called the opposite side because it is opposite the angle.
This side is called adjacent side because it is near the angle. θ A triangle in which one angle is a right angle is called a right triangle. In a right triangle, the three sides are given special names. a. The hypotenuse, which is the longest side, is the side opposite the 90° angle; and b. The remaining two sides are called the legs of the triangle. The two other sides are named in relation to another known angle (or unknown angle under consideration).
Lesson 3: Solution to Right Triangles
To solve