Trig Ratios

Trig Ratios

What is Trigonometry?

• Trigonometry is the study of the relationship between side lengths and angles in triangles.

• Study emerged in the Hellenistic (Greek) period during the 3rd Century BC

What are trig ratios?

• Trig ratios represent the relationship between sides and angles of a right triangle.

• There are six trig(onometric) ratios: sine, cosine, tangent, cotangent, secant, cosecant.

What are the three main trig ratios?

• The angle is sometimes represented as $\theta$  , a Greek letter

• sine ( $\theta$  ) = opposite side/hypotenuse

• cosine ( $\theta$  ) = adjacent side/hypotenuse

• tangent ( $\theta$  ) = opposite side/adjacent

How to Remember the Trig Ratios

• SOH CAH TOA

• SOH: sine = opposite over hypotenuse

• CAH: cosine = adjacent over hypotenuse

• TOA: tangent = opposite over adjacent

How to Label the Sides of a Triangle for Trig Ratios

• The label of the side will change with respect to the angle of interest

• Label the hypotenuse 1st: It is the side opposite the right angle

• Label the opposite side next: Start at the vertex of the angle and draw a line as if bisecting the angle straight to the side acoss.

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How to Label the Sides of a Right Triangle for Trig Ratios

• adjacent: if you label the hypotenuse first, and the opposite next, then the adjacent would be the remaining side.

• adjacent: one of the sides that forms the angle that is not the hypotenuse.

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Sine (abbreviated sin)

• opposite side/hypotenuse

• ratios can also be represented as a function with the angle as the input and the value of the sin as output.

Sin ( $\theta$  )

• Sin ( $\theta$  ) = opposite/hypotenuse

• Sin ( $\theta$  ) = AB/AC

sin ( $\theta$  )

• Opposite side/hypotenuse

• = 15/17 or .88

Cosine ( $\theta$  )

• adjacent side / hypotenuse

• ratios can also be represented as a function with the angle as the input and the value of the sin as output.

Cosine (abbreviated cos)

• adjacent / hypotenuse

Cosine ( $\theta$  )

• adjacent/hypotenuse

• hypotenuse = 9

• adjacent side = 6

• cosine (  $\theta$ )  = adjacent/hypotenuse 

• cosine (  $\theta$ )  = 6/9 = 2/3 = .67

Cosine ( $\theta$  )

• Angle L: opposite side = 6, hypotenuse = 10, adjacent = 8. Cosine (L) = adjacent/hypotenuse = 8/10 = 4/5 = .8

• Angle N: opposite side = 8, adjacent side = 6, hypotenuse = 10. Cosine (N) = adjacent /hypotenuse = 6/10 = 3/5 = .6

Tangent ( $\theta$  )

• Tangent ( $\theta$  ) = opposite/adjacent

• ratios can also be represented as a function with the angle as the input and the value of the sin as output.

Tangent (θ)

• opposite side/adjacent side

Tangent (θ)

• Label the hypotenuse: 5

• Label the opposite side: Side opposite  $\theta$  is 4.

• Label the adjacent side: 3

• Tangent = opposite/adjacent = 4/3 = 1.33

Multiple Choice

• 9/41

• 40/41

• 9/40

• 3/10

Multiple Choice

Give the Ratio for COS X

• Adj/Hyp
• Opp/Adj
• Adj/Opp
• Opp/Hyp

Multiple Choice

Give the Ratio for SIN X

• Opp/Adj

• Adj/Hyp

• Opp/Hyp

• Adj/Opp

Multiple Choice

Choose the correct ratio.

• sin(37)=x/14

• cos(37)=x/14

• tan(37)=x/14

• sin(37)=14/x

Multiple Choice

Choose the correct ratio.

• cos(33)=x/14

• sin(33)=x/14

• cos(33)=14/x

• sin(33)=14/x

Multiple Choice

Find Cos(A) as a decimal rounded the the nearest ten-thousandth.

• .4706

• 1.875

• .8824

• .5333

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

If you are given the hypotenuse and an adjacent side, which trig function should you use?

• sine
• cosine
• tangent

Multiple Choice

If you are given the opposite side and hypotenuse, which trig function should you use?

• sine
• cosine
• tangent

Multiple Choice

If you are given the two sides that are not the hypotenuse, which trig function should you use?

• sine
• cosine
• tangent

Multiple Choice

From ∠C, what side is AB?

• Adjacent

• Hypotenuse

• Opposite

Multiple Choice

Which one is the easy way to remember trigonometric ratios?

• Sah Coh Toa

• Soh Cah Toa

• Soh Cah Tao

• Soh Ceh Toa

Multiple Choice

Which one is the easy way to remember trigonometric ratios?

• Sah Coh Toa

• Soh Cah Toa

• Soh Cah Tao

• Soh Ceh Toa