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Today we will be learning:
-How to evaluate trigonometric
functions of acute angles.
-How to use the fundamental
trigonometric identities.
Lesson 1.3 Rt.  Trigonometry
Sin  = opp/hyp
Opposite
Side

Csc  = hyp/opp
SOH CAH TOA
Ex 1: Find the exact values of the six Trig functions of the angle 
shown in the figure. (Use the Pythagorean Theorem to
find the third side of the triangle.)
Hyp =
13
5

5
sin  =
13
cos  =
5
tan  =
12
12
12
13
13
csc  =
5
sec  =
12
cot  =
5
13
12
1
2

sin 45º =
2
2
45º
2
1
45º
1
2

cos 45º =
2
2
tan 45º =
1
1
1
sin 30º = sin /6 = 2
30º
2
60º
1
3
cos 30º = cos /6 =
3
2
1
3
tan 30º = tan /6 =

3
3
3
sin 60º = sin /3 =
2
1
cos 60º = cos /3 =
2
tan 60º = tan /3 =
3
Co-functions of complementary angles are equal.
sin 30º =
1
2
= cos 60 º
cos 30º =
3
2
= sin 60 º
Co-function Pairs
sin & cos
tan & cot
csc & sec
Ex 2: Find the exact values of the six Trig functions of
the angle  for each of the two triangles.
3
5

4
sin  = 3/5
cos  = 4/5
tan  = 3/4
csc  = 5/3
sec  = 5/4
cot  = 4/3
1.5
2.5  sin  = 1.5/2.5 = 3/5
2.0
cos  = 2.0/2.5 = 4/5
tan  = 3/4
csc  = 5/3
sec  = 5/4
cot  = 4/3
Ex 3: Sketch a right triangle corresponding to the trig
function of the acute angle . Use the Pyth. Thm. to
determine the third side, then find the other five trig
functions of .
A. sin  = 3/4
cos  =
7
4
3 3 7
tan  =
7
7
4
3
4
csc  = 3

√7
7
cot  =
3
4
4 7
sec  = 7  7
Ex 3(cont’d): Sketch a right triangle corresponding to the
trig function of the acute angle . Use the Pyth. Thm. to
determine the third side, then find the other five trig
functions of .
B. cot  = 3/2
2
2 13

sin  =
13
13
cos  =
3
3 13

13
13
Homework: p. 156 #2-16 even
√13
2

2
tan  =
3
csc  =
sec  =
3
13
2
13
3
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