Aim:

1
Aim What does SOHCAHTOA have to do with our
study of right triangles?
Do Now
What are the following ratios?
Key terms adjacent, opposite hypotenuse
2
Trigonometry Basics - Sine
In a right DABC with right angle ?BCA

• The sine of angle B, written sine B,
  is defined as

AC
sin B

3
Sines Reciprocal
What is the reciprocal of sin??
1/sin ?
What is the reciprocal of 3?
1/3
cosecant
the reciprocal of sin? has a special name
csc ? ?

ex.
using the calculator to find csc 53º
Method 1
find csc 53º
53
ENTER
sin
x -1
ENTER
Display 1.252135658
4
Trigonometry Basics - Cosecant
In a right DABC with right angle ?BCA

• The cosecant of angle B, written csc B,
  is defined as

AB
csc B

5
Trigonometry Basics - Cosine
In a right DABC with right angle ? BCA

• The cosine of angle B, written cos B,
  is defined as

BC
cos B

the sine of an acute angle has the same value as
the cosine of its complement.
Recall
6
Cosines Reciprocal
The reciprocal of cosine ? is the secant ?
sec ? ?
2
ex.
7
Trigonometry Basics - Secant
In a right DABC with right angle ? BCA

• The secant of angle B, written sec B,
  is defined as

AB
sec B

8
Trigonometry Basics - Tangent
In a right DABC with right angle ? BCA

• The tangent of angle B, written tan B,
  is defined as

AC
tan B

9
Tangents Reciprocal
The reciprocal of tan ? is the cotangent ?
cot ? ?

ex.
tan ?
10
Trigonometry Basics - Cotangent
In a right DABC with right angle ? BCA

• The cotangent of angle B, written cot B,
  is defined as

BC
cot B

11
Meet Chief
SOH
CAH
TOA
12
Trig. Relationships
Recall
the sine of an acute angle has the same value as
the cosine of its complement.
sin A cos B and cos A sin B
the tangent of an acute angle has the same value
as the cotangent of its complement.
tan A cot B and cot A tan B
The tangent of an acute angle is the reciprocal
of the tangent of its complement
tan A tan B 1
13
Model Problem
In right triangle ABC with right angle at C, BC
6, and AC 8. Find the three trigonometric
functions of ? B.
A
10
8
B
C
6
sin B
cos B
tan B
14
Model Problem
Park planners would like to build a bridge across
a creek. Surveyors have determined that from 5
ft. above the ground the angle of elevation to
the top of an 8ft. pole on the opposite side of
the creek is 5o. Find the length of the bridge
to the nearest foot.
5o
x
5
8
15
Model Problems

• sin 24o is equivalent to
• a) cos 24o b) sin 66o c) cos 660 d)
  1/sin 240

The sine of an angle has the same value as the
cosine of its complement.
2. If cot x tan(x 20o), find x.
When the cotangent and tangent functions are
equal in value, the angles must be complementary.
x (x 20) 90
2x 20 90
x 70
16
Degrees, Minutes Seconds
3600 in a circle
60 minutes in 1 degree
1 minute is 1/60th of a degree
60 seconds in 1 minute
1 second is 1/60th of a minute
17o 4305
17 degrees 43 minutes 5 seconds
17
Model Problem
Find cos 17o 43 to 4 decimal places
Find sin 20.30o to 4 decimal places
Find sin 20o 30 to 4 decimal places
18
Find An Angle Given a Trig Function Value
What is measure of ??
Calculators MODE must be in degrees
30o
What is measure of ??
19
Regents Prep
In triangle ABC, side a 7, b 6, and c 8.
Find m? B to the nearest degree.
1) 43o 2) 47o 3) 65o 4) 137o
20
Regents Prep
In the diagram below of right triangle KTW, KW
6, KT 5, and m?KTW 90.

• What is the measure of ?K, to the nearest minute?
• 33o33 2) 33o55
• 3) 33o34 4) 33o56