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Sec. 13-1
Right Angle Trigonometry
A _________________________ is a function whose rule is given by a trig. ratio.
A trig. Ratio compares the ___________________________________________.
The greek letter ____________ is traditionally used to represent the measure of an
______________________ in a right triangle.
Special Right Triangles
45-45-90 Triangle Theorem
In any 45-45-90 triangle, the length of the ____________________ is
________________________________.
30-60-90 Triangle Theorem
In any 30-60-90 triangle, the length of the hypotenuse is 2 times the length of the
_________________________, and the length of the ____________________ is 3
times the length of the shorter leg.
Ex. 1
Find the unknown side lengths for the triangle shown.
Trig. Functions
The sine (sin) of angle 0 is the ratio of the length of the ______________________ to
the length of the ___________________.
The cosine (cos) of angle 0 is the ratio of the length of the __________________ leg
to the length of the ___________________.
The tangent (tan) of angle 0 is the ratio of the length of the _____________________
to the length of the ____________________.
Ex. 2
Finding Trig. Ratios
Find the value of the sine, cosine, and tangent functions for 0.
Recall from geometry that in a 30-60-90 triangle, the ratio of the side lengths is
___________________
In a 45-45-90 triangle, the ratio of the side lengths is ____________________
Trig. Ratios of Special Right Triangles
Sin 30 =
Cos 30 =
Tan 30 =
Sin 60 =
Cos 60 =
Tan 60 =
Sin 45 =
Cos 45 =
Tan 45 =
Ex. 3 Finding side lengths of special right triangles
Use a trig. function to find the value of x.
The reciprocals of the sine, cosine, and tangent ratios are also trigonometric ratios.
The cosecant (csc) of angle 0 is the _______________________________.
The _____________(sec) of angle 0 is the reciprocal of the ________ function.
The cotangent (cot) of angle 0 is the reciprocal of the _______________ function.
Ex. 4
Finding All Trig. Ratios
Find the values of the six trig. functions for 0.