1. The length of the Hypotenuse. The length of the Hypotenuse.
Right triangle trigonometry definitions.
Build a right triangle in the diagram over the central angle.
Label the right triangle.
c is the HYPOTENUSE.
a is the side OPPOSITE of .
Label the right triangle using theta( ) as the reference angle.
This angle is always ACUTE!
b is the side ADJACENT to .
SOH-CAH-TOA
The length Opposite of
The length of the Hypotenuse. I N E P O S I T E Y P O T E N U S O S I N E D J A C E N T Y P O T E N U S A N G E T P O S I T E D J A C E N T
The length Adjacent of
The length of the Hypotenuse.
The length Opposite of
The length Adjacent of

2. The length of the Hypotenuse. The length of the Hypotenuse.
Right triangle trigonometry definitions.
REMEMBER
Pythagorean Theorem
Build a right triangle in the diagram over the central angle.
Label the right triangle.
c is the HYPOTENUSE.
a is the side
Label the right triangle using theta( ) as the reference angle.
This angle is always ACUTE!
ADJACENT
OPPOSITE
of .
b is the side
ADJACENT
OPPOSITE
of .
The length of
The length of the Hypotenuse.
Opposite
SOH-CAH-TOA I N E P O S I T E Y P O T E N U S O S I N E D J A C E N T Y P O T E N U S A N G E T P O S I T E D J A C E N T
The length of
The length of the Hypotenuse.
Adjacent
The length of
Opposite
The length of
Adjacent

3. SOH-CAH-TOA Find the 6 trigonometric functions with respect to .
Circle the reference angle and label the opposite, adjacent, and hypotenuse.
Find the value of the missing side, c.
HYP.
OPP.
ADJ.
SOH-CAH-TOA

4. Special Right Triangle Relationships.
These answers are considered exact values.

5. Special Right Triangle Relationships.

6. Do you see a pattern?

7. Cofunction Identities.
Two positive angles are complimentary if their sum is 90o. Our trigonometric functions are identified with the prefix “Co”.
Sine & Cosine
Tangent & Cotangent
Secant & Cosecant
From the Ex.

9. Definition of Reference Angle.
Let be a nonacute angle in standard position that lies in a quadrant. Its reference angle is the positive acute angle formed by the terminal side of and the x – axis.

10. Find all six trigonometric function exact values of
Use special right triangles and reference angles to find the exact values of the trigonometric functions.
SOH – CAH - TOA
S A
T C
adj
Reference angle
opp
hyp

11. Use special right triangles and reference angles to find the exact values of the trigonometric functions.
SOH – CAH - TOA
S A
T C
hyp
S A
T C
opp
adj
Reference angle
Reference angle
opp
adj
hyp

12. S A T C S A T C S A T C S A T C hyp hyp opp adj opp Reference angle
Give away for 45o angle
S A
T C

13. MODE
Right now we want DEGREE mode, move cursor to DEGREE and hit ENTER
2nd APPS activate the ANGLE window.
Degree symbol.
Minute symbol.
x-1 button
Second symbol.
ALPHA, +

15. hyp. opp. Find angles first. SOH-CAH-TOA adj. right C acute A B
complimentary
hyp.
opp.
Find angles first.
SOH-CAH-TOA
adj.

16. hyp. opp. adj. SOH-CAH-TOA Need to find the following: = 29.43 = 53.58
44.77
adj.
A general rule is to always use the information you are given. We can find b by the Pythagorean Theorem.
SOH-CAH-TOA
Make sure the MODE is DEGREE.
Sides were given to 2 decimal places … so b = 44.77

17. SOH-CAH-TOA
hyp. y =
opp. x =
adj.
adj.
opp.
hyp.

18. When a single angle is given, it is understood that the
Bearing is measured in a clockwise direction from due north. N N N
45o
165o
225o
Starts at a Bearing starting on the north-south line
and uses an acute angle to show the direction, either east or west.
S 45o E
N 75o W N
45o
75o S

19. SOH-CAH-TOA
adj.
opp.
61o
331o
hyp.

20. 43o
3.5(22) = 77
4(22) = 88
47o

21. hyp.
opp.
opp.
hyp.
SOH-CAH-TOA
adj.
adj.
Solve for x to find h.