Vocabulary
Sine Function- If θ is and acute angle of a right triangle, the sine of θ is the length of the side opposite θ divided by the length of the hypotenuse. Cosine Function- If θ is an acute angle of a right triangle, the cosine of θ is the length of the side adjacent to θ divided by the length of the hypotenuse.
Tangent Function- If θ is an acute angle of a right triangle, the tangent of θ is the length of the side opposite to θ divided by the length of the side adjacent to θ.
Cosecant Function- If θ is an acute angle of a right triangle, the cosecant of θ is the length of the hypotenuse to θ divided by the length of the side opposite θ.
Secant Function- If θ is an acute angle of a right triangle, the secant of θ is the length of the hypotenuse to θ divided by the length of the adjacent to θ.
Cotangent Function- If θ is an acute angle of a right triangle, the cosine of θ is the length of the side adjacent to θ divided by θthe length of the hypotenuse.
Tangent Function- If θ is an acute angle of a right triangle, the tangent of θ is the length of the side opposite to θ divided by the length of the side adjacent to θ.
Cosecant Function- If θ is an acute angle of a right triangle, the cosecant of θ is the length of the hypotenuse to θ divided by the length of the side opposite θ.
Secant Function- If θ is an acute angle of a right triangle, the secant of θ is the length of the hypotenuse to θ divided by the length of the adjacent to θ.
Cotangent Function- If θ is an acute angle of a right triangle, the cosine of θ is the length of the side adjacent to θ divided by θthe length of the hypotenuse.
Essential Information
A right triangle has an acute angle θ ( the Greek letter theta). The three sides of the triangle are the hypotenuse, the side opposite θ, and the side adjacent to θ.
Ratios of a right triangle's side lengths are used to define the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. These six functions are abbreviated sin, cos, tan, csc, sec, cot. |
Right Triangle Definitions of Trigonometric Functions
Let θ be an acute angle of a right triangle. The six trigonometric functions of θ:
Let θ be an acute angle of a right triangle. The six trigonometric functions of θ:
The abbreviations opp, adj, and hyp are often used to represent the side lengths of the right triangle. The ratios in the second row are reciprocals of those in the first.
Special Angles
The angles 30⁰, 45⁰, and 60⁰ occur frequently in trigonometry.The trigonometric values for these angles can be used to find unknown side lengths in special right triangles.
The angles 30⁰, 45⁰, and 60⁰ occur frequently in trigonometry.The trigonometric values for these angles can be used to find unknown side lengths in special right triangles.
Solving a TriangleFinding all unknown side lengths and angle measures of a triangle is called solving a triangle. Solving right triangles that have acute angles other than 30⁰, 45⁰, 60⁰ may require the use of a calculator.
To find values of the sine, cosine and tangent functions on a calculator, use the keys sin, cos, and tan. Make sure the calculator is set in degree mode.
To find values of the sine, cosine and tangent functions on a calculator, use the keys sin, cos, and tan. Make sure the calculator is set in degree mode.
Angles of Sight
If a point above is viewed, the angle that the line of sight makes with a line parallel to the ground is called the angle of elevation. At the point above, the angle between a line parallel to the ground and the line of the point at the ground is called the angle of depression. The two angles have the same measure. |