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 .

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

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

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

Special Right Triangle Relationships.

Do you see a pattern?

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 30-60-90 Ex.

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.

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

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

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

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 0.7571217563 -7.205879213 -0.4067366431 1.253948151 Second symbol. ALPHA, +

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

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

SOH-CAH-TOA hyp. y = 57.635 opp. x = 68.687 adj. adj. opp. hyp.

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

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

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

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