Trigonometric Ratios

A RATIO is a comparison of two numbers. For example; boys to girls cats : dogs right : wrong.

In Trigonometry, the comparison is between sides of a triangle .

Name “say”

Sine

Trig. Ratios

Cosine tangent

Abbreviation Abbrev.

Sin Cos Tan

Ratio of an angle measure

Sin θ = opposite side hypotenuse cosθ = adjacent side hypotenuse tan θ =opposite side adjacent side

Three Trigonometric Ratios

• Sine – abbreviated ‘sin’. – Ratio: sin θ = opposite side hypotenuse

Θ

this is the symbol for an unknown angle measure. It’s name is ‘Theta’.

• Cosine - abbreviated ‘cos’. – Ratio: cos θ = adjacent side hypotenuse Easy way to remember trig ratios: SOH CAH TOA • Tangent - abbreviated ‘tan’. – Ratio: tan θ = opposite side adjacent side

B a c

Let’s practice…

Write the ratio for sin A Sin A =

o

= a

h

c Write the ratio for cos A Cos A =

a

= b

h

c C b A Let’s switch angles: Find the sin, cos and tan for Angle B: Write the ratio for tan A Tan A =

o

= a

a

b Sin B = b c Cos B = a c Tan B = b a

I want to find Use these calculator keys

Ratio of sides as a decimal A missing side Angle measure Regular keys SIN COS TAN SIN -1 COS -1 TAN -1 Make sure you have a calculator… To set your calculator to DEGREE: MODE (next to 2 nd button) Degree (third line down… highlight it) Enter 2 nd Quit

C 2cm

Let’s practice…

Find an angle that has a tangent (ratio) of 2 3 Round your answer to the nearest degree.

B 3cm A Process: I want to find an ANGLE I was given the sides (ratio) Tangent is opp adj TAN -1 (2/3) = 34 °

Practice some more…

Find tan A: 24.19 12 Tan A = opp/adj = 12/21 Tan A = .5714

A 21 Find tan A: Tan A = 8/4 = 2 4 A

Trigonometric Ratios

• When do we use them?

– On right triangles that are NOT 30-60-90 45-45-90 or Find: tan 45 1 Why?

tan = opp adj

Using trig ratios in equations

Remember back in 1 st grade when you had to solve: What did you do?

6 72 = x Remember back in 3rd grade when x was in the denominator?

What did you do?

x 12 12 x = 1/2

34 ° x cm 15 cm Ask yourself: In relation to the angle, what pieces do I have?

Opposite and hypotenuse Ask yourself: What trig ratio uses Opposite and Hypotenuse?

SINE Set up the equation and solve: (15)Sin 34 = x 8.39 cm = x 15

12 cm 53 ° x cm Ask yourself: In relation to the angle, what pieces do I have?

Opposite and adjacent Ask yourself: What trig ratio uses Opposite and adjacent?

tangent Set up the equation and solve: (12)tan 53 = x 15.92 cm = x 12

x cm 68 ° 18 cm Ask yourself: In relation to the angle, what pieces do I have?

Adjacent and hypotenuse Ask yourself: What trig ratio uses adjacent and hypotnuse?

cosine Set up the equation and solve: x cos 68 cos 68 X = 18 cos 68 X = 48.05 cm

22 cm 42 cm θ This time, you’re looking for theta. Ask yourself: In relation to the angle, what pieces do I have?

Opposite and hypotenuse Ask yourself: What trig ratio uses opposite and hypotenuse?

sine Set up the equation (remember you’re looking for theta): Sin θ = 22 42 Remember to use the inverse function when you find theta Sin -1 22 = θ 42 31.59

°= θ

You’re still looking for theta. 22 cm θ 17 cm Ask yourself: What trig ratio uses the parts I was given?

tangent Set it up, solve it, tell me what you get. tan θ = 17 22 tan -1 17 = θ 22 37.69

°= θ

Your assignment

Cannibal Trignometry wksht