Section 5.2 Trigonometric Function of Real Numbers Chapter 5 – Trigonometric Functions: Unit Circle Approach 5.2 - Trigonometric Function of Real Numbers
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5.2 - Trigonometric Function of Real Numbers
Section 5.2 Trigonometric
Function of Real Numbers
Chapter 5 – Trigonometric Functions: Unit Circle Approach
5.2 - Trigonometric Function of Real Numbers
Definition of the Trig Functions
5.2 - Trigonometric Function of Real Numbers
Example – pg. 384Find sin t and cos t for the values of t whose terminal
points are shown on the unit circle in the figure. t increases in increments of /4.
5.2 - Trigonometric Function of Real Numbers
Special Values
5.2 - Trigonometric Function of Real Numbers
Domains of the Trig Functions
Function Domainsin, cos All real numbers
tan, sec All real numbers other than for any integer n
cot, csc All real numbers other than n for any integer n
2n
5.2 - Trigonometric Function of Real Numbers
Signs of the Trig Functions
Quad Positive Functions Negative Functions I All None II sin, csc cos, sec, tan,
cot III tan, cot sin, csc, cos,
secIV cos, sec sin, csc, tan, cot
5.2 - Trigonometric Function of Real Numbers
Example – pg. 384Find the exact value of the trigonometric functions at
the given real number.
5.2 - Trigonometric Function of Real Numbers
Examples – pg. 385Find the sign of the expression if the terminal point
determined by t is in the given quadrant.
tan sin49. , Quadrant III
cot
50. cos sec , any quadrant
t t
t
t t
5.2 - Trigonometric Function of Real Numbers
Even-Odd PropertiesSine, cosecant, tangent, and cotangent are odd
functions.Cosine and secant are even functions.
sin sin cos cos tan tan
csc csc sec sec cot cot
t t t t t t
t t t t t t
5.2 - Trigonometric Function of Real Numbers
Example – pg. 384Find the exact value of the trigonometric functions at
the given real number.
5.2 - Trigonometric Function of Real Numbers
Fundamental Identities
Reciprocal Identities
Pythagorean Identities
1 1csc sec
sin cos
sin 1 costan cot =
cos tan sin
t tt t
t tt t
t t t
2 2 2 2 2 2sin cos 1 tan 1 sec 1+cot csct t t t t t
5.2 - Trigonometric Function of Real Numbers
Examples – pg. 385Write the first expression in terms of the second if the
terminal point determined by t is in the given quadrant.
5.2 - Trigonometric Function of Real Numbers
Examples – pg. 385Find the values of the trigonometric functions of t
from the given information.
5.2 - Trigonometric Function of Real Numbers
Examples – pg. 384Find the exact value of the trigonometric functions at
the given real number.
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