Lesson 9 1 9 2 Trigonometry of Right

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Lesson 9 -1 & 9 -2: Trigonometry of Right Triangles (Sine, Cosine, Tangent) SOH-CAH-TOA

Lesson 9 -1 & 9 -2: Trigonometry of Right Triangles (Sine, Cosine, Tangent) SOH-CAH-TOA

Using Trigonometry in Right Triangles Opposite Adjacent • Be able to find the ________,

Using Trigonometry in Right Triangles Opposite Adjacent • Be able to find the ________, Hypotenuse and _____ sides from an angle ____ Adjacent ____ Opposite Hypotenuse _______ Opposite ____ Adjacent Opposite Adjacent • _____ & _____ depend on where you start! Next to • Adjacent means “______” STAYS • Hypotenuse ______ hypotenuse

Trig Ratios Opposite Adjacent • Use _________, and Hypotenuse ______ to set up ratios

Trig Ratios Opposite Adjacent • Use _________, and Hypotenuse ______ to set up ratios (fractions) • These ratios are related to the size of Angle the_____ • Three Trig Functions Sine (sin) ______ Cosine (cos) ______ Find them on your calculator! Tangent (tan) ______ ALWAYS Sin, cos, tan are _____ talking about an angle!!!

Trig Ratios A 300 B ► SOH-CAH-TOA ______ 2 1 C

Trig Ratios A 300 B ► SOH-CAH-TOA ______ 2 1 C

Using calculator to find angles From the previous slide, solve for angle A: So:

Using calculator to find angles From the previous slide, solve for angle A: So: Inverse of sin is sin-1 angle fraction/decimal Sin of an ______ gives the __________ fraction/decimal angle Sin-1 of an __________ gives the ______

Using Trig • Finding a missing side missing 1. Label the angle, given side,

Using Trig • Finding a missing side missing 1. Label the angle, given side, and ______ side (x) 2. Draw a _______ by the angle stick figure adjacent 3. Identify the given and missing sides using ______, opposite hypotenuse _______, and _________ SOH-CAH-TOA 4. Choose 1 of the 3 equations from: _________ 5. Fill in equation with numbers and x proportion (sin, cos, tan can be over “ 1”) 6. Solve using a _____ • Finding a missing angle given 2 sides 1. Follow steps 1 – 5 above, then inverse 2. Solve for the angle by using the _____ trig function with the fraction/decimal →

Find sin L, cos L, tan L, sin N, cos N, and tan N.

Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal.

Answer:

Answer:

EXERCISING A fitness trainer sets the incline on a treadmill to The walking surface

EXERCISING A fitness trainer sets the incline on a treadmill to The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches.

Proportion: Multiply sin 70 by 60, divide by 1 if you want to KEYSTROKES:

Proportion: Multiply sin 70 by 60, divide by 1 if you want to KEYSTROKES: SIN 7 X 60 ENTER 7. 312160604 Answer: The treadmill is about 7. 3 inches high.