Test grades will be in Wed afternoon Test corrections Thu, Fri, Mon am and pm Retakes Thu, Fri, Mon pm ONLY Pick up trig packet.

Test grades will be in Wed afternoonTest corrections Thu, Fri, Mon am and

pmRetakes Thu, Fri, Mon pm ONLY

Pick up trig packet

10/2 Test grades were posted Wed afternoon

Test corrections Thu, Fri, Mon am and pmRetakes Thu, Fri, Mon pm ONLY. End of six weeks is Friday

Yesterday we reviewed trig. The notes are on line. We began the trig packet

Today you will complete trig packet. It is due at the EOC.

Pay attention to units: all sides must match! 1inch = 2.54 cm

What does it mean to say “as the crow flies”?

What does it mean to say “as the crow flies”?

What is the Pythagorean Theorem?

c2 = a2 + b2

Side labels

L

K

J

Name the sides

L adj

K opp

J hyp

Name the sides

SOH CAH TOA

b

csin

opp

hyp

cos adj

hypa

c

tan opp

adjb

a

c a b2 2 2

• What does Sin θ stand for?• Ratio of Opposite / Hypotenuse for a given angle

• What does Cos θ stand for?• Ratio of Adjacent / Hypotenuse for a given angle

• What does Tan θ stand for?• Ratio of Opposite / Adjacent for a given angle

.5934 34 .5592 .8290 .6745 1.7883 1.2062 1.4826 56 .9774

.6109 35 .5736 .8192 .7002 1.7434 1.2208 1.4281 55 .9599

.6283 36 .5878 .8090 .7265 1.7013 1.2361 1.3764 54 .9425

.6458 37 .6018 .7986 .7536 1.6616 1.2521 1.3270 53 .9250

.6632 38 .6157 .7880 .7813 1.6243 1.2690 1.2799 52 .9076

.6807 39 .6293 .7771 .8098 1.5890 1.2868 1.2349 51 .8901

.6981 40 .6428 .7660 .8391 1.5557 1.3054 1.1918 50 .8727

.7156 41 .6561 .7547 .8693 1.5243 1.3250 1.1504 49 .8552

.7330 42 .6691 .7431 .9004 1.4945 1.3456 1.1106 48 .8378

.7505 43 .6820 .7314 .9325 1.4663 1.3673 1.0724 47 .8203

.7679 44 .6947 .7193 .9657 1.4396 1.3902 1.0355 46 .8029

.7854 45 .7071 .7071 1.0000 1.4142 1.4142 1.0000 45 .7854

Cos Sin Cot Sec Csc Tan Deg Rad

• Find the tan for the given angle

• First name the sides

• Tan = Opp/Adj = 11.2 cm/8.4 cm = 1.33

8.4 cm

11.2 cm

14 cm

Use tan function to fin the tan (ie. The ratio)

Tan (53.13º)

Tan (53.13º) = 1.333

Use inverse tan function to find the angle if

Tanθ = 1.333

Tan-1(1.333) = 53.12º

We have looked at:• Pythagoreans• Naming sides• Determining ratios• Determining sides• Determining angles

Summary Ratios:

sinθ , cosθ and tanθ describe ratio of two sides. No unit.•Can determine two ways(ex with sin):

– Knowing the angle: sin(30º) = 0.5 – Knowing the sides: sin θ= Opp/Hyp sin θ

=5m/10m = .5

5m

10m

30º

Summary Angles:

To find angles use the inverse of the appropiate function:sin-1 , cos-1 and tan-1

•Can determine two ways(ex with sin):– Knowing the sides: sin-1 (5m/10m)= 30º – Knowing the ratio: sin-1 (.5)= 30º

5m

10m

30º

Summary Putting it all together:

If you need to determine a side:

•Name sides in reference to known angle

•Determine formulaYou know angle and hypotenuse, want opposite: Opp = (sinθ)(Hyp)(sin30º)(10m) = 5m

?? opp

10m hyp

30º

Summary Putting it all together:

If you need to determine an angle :

•Name sides in reference to angle of interest

•Determine formula– You know opp and hypotenuse, want θ :

sin-1 = (Opp/Hyp)– sin-1 (5m/10m)=30º

5m opp

10m hyp

Θ ??

1. 32 m

55º

= 26.21 m

a c b 2 2

32 26 22 2.

c a b2 2 2

= 18.36 m a = 18.36 mb = 26.21 m

Sin 55° = a

b B32 m

B = (32 m)(sin 55°)

To solve for a…

Find R and Ө.

2.

Finding a sideThe Church Steeple

Eric decides to find the height of the steeple of his local church. He measures a distance of 50. m along the ground. The angle of elevation of the top of the steeple is 35°in reference to the ground. How high is the steeple?

Step 1. Draw a diagram.

50.m 35°

?

The Church Steeple

?

50m

35°

Have the Adjacent side and an angleWant the Opposite side. Use tan = opp/adj

Opp = (tan adj)

Opposite= (tan 35°)(50m)= 35 m

Finding An Angle The Airplane

At Bush IAH airport there is a forest just 500. m from the end of the runway. The trees can be as tall as 30. m. What is the minimum angle of climb if aircraft are to avoid the trees?

Step 1. Draw a diagram.

30.m

500.m?

Finding An Angle30

500

Have the Adjacent and Opposite sides Want the angleUse tan = opp/adjTo find angles need to use tan-1

tan-1 (30m/500m) = 3.4º