“Success in math is considered a gateway to many educational and occupational opportunities”. (Jetter, 1993)

GRANT UNION HIGH SCHOOL

• Title I school

• 2,000 – 2,200 student population

• 90% of students have free lunch (low social economic status)

• 40% of student population are English Language Learners (Hispanic; Hmong and Lao refugees)are Special Education

• At least 30% of students don’t live with parents (foster home, relatives)

• Math skills of at least 50% of student population is 1 to 2 grade levels behind

COLLABORATION GOALS

• 70% of students in each class achieve in math

• Weekly collaboration to discuss lesson delivery, teaching strategies, assessment results, and make revisions to plans as needed

• Standards-driven reform is the primary approach

• Activate student conceptual knowledge when presented with a real-life problem solving situation

• Improve student motivation, participation, and generalization skills of students

TEACHER COLLABORATION

• Involves teachers of same subject matter

• Weekly collaboration to discuss lesson delivery, teaching strategies, assessment results, and make revisions to plans as needed

• Standards-driven reform is the primary approach

• Planning for curriculum, pacing, common formative assessments, sharing of best practices during summer break

TRIGONOMETRY

三角法 GREEK WORD MEANING:

在希腊的词汇中就是指：

TRIANGLE

MEASURE

三角形计算

IN 140 B.C. HIPPARCHUS

BEGAN TO USE AND WRITE

TRIGONOMETRY在公元前 140 年希帕庫斯

（ Hipparchus ）就已经开始使用三角法并撰写相关著作了。

ANCIENT GREEKS USED

TRIGONOMETRY TO MEASURE THE DISTANCE TO THE

STARS古希腊人曾使用三角法计算地球到恒星的距离。

OBJECTIVES:

1. TO FIND TRIGOMETRIC RATIOS OF A RIGHT TRIANGLE.

2. TO FIND VALUES OF TRIGOMETRIC FUNCTIONS.

3. TO APPLY THE TRIGOMETRIC FUNCTIONS TO SOLVE RIGHT -TRIANGLE

PROBLEMS.

90

•WE WILL DEAL ONLY WITH RIGHT TRIANGLES

RIGHT TRIANGLES MUST HAVE A 90 DEGREE ANGLE

我们将只对直角三角形进行说明

直角三角形必须有一个 90 度的角。

HYPOTENUSE

LEG ADJACENT TO ANGLE B

LEG OPPOSITE TO B

B

角 B的对边

斜边

角 B的邻边

LEG ADJACENT TO B

LEG OPPOSITE TO B

HYPOTENUSE

SINE OF B = LENGTH OF LEG OPPOSITE B LENGTH OF HYPOTENUSE

COSINE OF B = LENGTH OF LEG ADJACENT TO B

LENGTH OF HYPOTENUSE

TANGENT OF B = LENGTH OF LEG OPPOSITE B

LENGTH OF LEG ADJACENT TO B

B

角 B的邻边

角 B的对边斜边

sinB = 角 B对边长 /斜边长

cosB = 角 B邻边长 /斜边长

tanB = 角 B对边长 /角 B邻边长

B

SAMPLE RIGHT TRIANGLE PROBLEMS

直角三角形例子

a

cb

Ø

A.) sin Ø = _______

B.) cos Ø = _______

C.) tan Ø = _______

1.) x

yz

20

30 60

Find the values to the nearest tenth of:

A.) XY = ________

B.) YZ = ________

b/c

a/c

b/a

11.5

23.1

To avoid a steep descent, a plane flying at 30,000 ft. starts its descent 130 miles away from the airport. For the angle of descent Ø, to be constant, at what angle should the plane descend?

APPLICATIONS:

一个飞机在 30,000 英尺的高空飞行，为避免急剧下降，要从离机场 130 英里的时候开始降落。下降时与地面的角度 Ø一定 , 求 Ø?

应用：

Ø

130 Miles

30,000 ft.

Ø

tan Ø = 30,0005,280*130

An observer 5.2 km from a launch pad observes a rocket ascending.

A. At a particular time the angle of elevation is 37 degrees. How high is the rocket?

B. How far is the observer from the rocket?

C. What will the angle of elevation be when the rocket reaches 30 km?

A. Tan 37 = a_

B. Cos 37 = 5.2

C. Tan = 30Ø

5.2

b

5.2

37

ba

5.2

一个观测员在离发射台 5.2 km 的地方观测火箭升空。

A. 在某一时刻，仰角是 37 度，这时火箭离地面多高？

B. 这一时刻观测员离火箭多远？

C. 当火箭到达 30 km 高空时，仰角是多少？

A. How far north of its original position is the ship?

B. How far east of its original position is the ship?

A ship sails 340 kilometers on a bearing of 75 degrees.

A. 这只船距原来位置的北方多远？

B. 这只船距原来位置的东方多远？

一只船朝东北方向 75 度航行了 340km.

b

a

75

340

A. Cos 75 = a 340

B. Sin 75 = b 340

BY THE STUDY OF TRIGONOMETRY----------

YOU TOO COULD REACH FOR THE STARS!!!!!!!!!!!

BE A ROCKET!!!!!!!

REACH FOR THE STARS!

BY THE STUDY OF TRIGONOMETRY----------

YOU TOO COULD REACH FOR THE STARS!!!!!!!!!!!

BE A ROCKET!!!!!!!

REACH FOR THE STARS!

APPLICATION ACTIVITY

TRIGONOMETRY PROJECT

with CLINOMETER WORKSHET