pre-calc book section 5.2 trigonometric functions of real numbers objectives: how do you find the...
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Pre-Calc Book Section 5.2Trigonometric Functions
of Real Numbers
Objectives:• How do you find the value of any given trig angle?• How can understanding the signs of the quadrants help in finding the function value of any trig angle?
Trigonometric Functions of Any Angle
siny
r
cosx
r
tan , 0yx
x
csc , 0ry
y
sec , 0rx
x
cot , 0xy
y
Ex. 1 Find the six trig functions of each given real number t.
a)
b)
6t
2t
Ex.2 Let be a point on the terminal side of . Find the sine, cosine, and tangent of .
1 3,2 2
Ex.3 Let (-3,4) be a point on the terminal side of . Find the sine, cosine, and tangent of .
Signs of Trig Functions
Quad PositiveIIIIIIIV
, ,
, ,
All Students Take Calculus
All Trig. Functions
Sine/Cosecant
Tangent/Cotangent
Cosine/Secant
Ex. 4 Determine the sign of the following trig functions.
a)
b)
c)
cos3
tan 4
7sin
4
> 0, because the terminal point of is in Quad I3
t
> 0, because the terminal point of is in Quad III4t
< 0, because the terminal point of is in Quad IV
7
4t
Class WorkFind the six trig functions of each given real number t.
1. 2. 4
t
3
t
Determine the sign of the following trig functions.
3.
4.
5.
5tan
6
cos7
5csc
4
Ex 5. Evaluate the sine, cosine and tangent of the given angle.
) 570a
) 60b
13)4
c
11)3
d
Ex. 6 Find the exact value of the trig function at the given real number t.
a)
b)
c)
2cos
3
tan3
19sin
4
d)
e)
f)
2cos
3
5sin
3
5tan
6
Class WorkFind the exact value of the trig function at the given real number t.
6.
7.
8.
5sin
6
4tan
3
14cos
3
Ex.7 State the quadrant in which lies.
) cos 0, sin 0a
) sec 0, tan 0b
) sin 0, cot 0c
Fundamental Identites
Ex 8. If and t is in quadrant IV, find the
values of all the trig functions at t.
3cos
5t
Ex 9. Find the values of the six trig functions of in the given quadrant.
5) tan cos 0
4a
) csc 3 tan 0b
2) sin cot 0
7c
Class WorkFind the values of all the trig functions of t from the given information.
13. In quad III
14. In quad III
15. sint < 0
4cos
5t
1tan
4t
sec 2t
HW #3 p.416 3-19 eoo, 27-35 eoo, 63-69 odd