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TRIGONOMETRY

Yvonne M. Conley, SSND Roman Catholic HS

Philadelphia, PA September 1999

General Information

- Trigonometry
- is the mathematics of right triangles.
- can be used to determine unknown distances that

are not easily measured with a ruler. - can be used to determine an unknown angle.
- there are six standard functions
- sin (sine) cos (cosine)
- tan (tangent) cot (cotangent)
- sec (secant) csc (cosecant)

Trigonometric Functions

opposite side

R

Y

angle of interest

q

X

adjacent side

adjacent

opposite

Y

X

cos q

sin q

R

R

hypotenuse

hypotenuse

opposite

Y

tan q

X

adjacent

b

adjacent side

angle of interest

R

Y

X

opposite side

adjacent

opposite

Y

X

cos b

sin b

R

hypotenuse

hypotenuse

R

opposite

X

tan b

Y

adjacent

Problem-Solving Strategy

Draw a right triangle. Write in the data provided

including units. Write the question. Write an

equation. Solve the problem.

Sample Problems

b

Calculate the sin of q and the sin of b.

25.0 m

20.0 m

q

15.O m

sin q ?

sin b ?

x/r

sin b

sin q

y/r

sin q 20.0 m/ 25.0 m

sin b 15.0 m/ 25.0 m

sin q 0.800

sin b 0.600

b

Calculate the cos of q and the cos of b.

25.0 m

20.0 m

q

15.O m

cos q ?

cos b ?

x/r

cos q

y/r

cos b

cos q 15.0 m/ 25.0 m

cos b 20.0 m/ 25.0 m

cos q 0.600

cos b 0.800

b

Calculate the tangent of q and the tangent of b.

25.0 m

20.0 m

q

15.O m

tan q ?

tan b ?

y/x

tan q

x/y

tan b

tan q 20.0 m/ 15.0 m

tan b 15.0 m/ 20.0 m

tan q 1.33 ...

tan b 0.750

Using the inverse of the trig. functions,

determine angle q .

b

25.0 m

20.0 m

tan-1 y/x q

tan-1 20.0m/15.0m q

q

53.1o q

15.O m

sin-1 y/r

q

cos-1 x/r q

cos-1 15.0m/25.0m q

sin-1 20.0m/25.0m q

53.1o q

53.1o q

Using the inverse of the trig. functions,

determine angle b .

b

25.0 m

20.0 m

tan-1 x/y b

tan-1 15.0m/20.0m b

q

15.O m

36.9o b

sin-1 x/r

b

cos-1 y/r b

cos-1 20.0m/25.0m b

sin-1 15.0m/25.0m b

36.9o b

36.9o b

Determine the length of an unknown distance x.

b

25.0 m

sin q y/r cos q x/r tan q y/x

?? m

q 30.0 o

?? m

tan q y/x

x y/ tan q

x 25.0 m/ tan 30.0 o

x 43.3 m

x 25.0 m / 0.577

b

Calculate the tangent of q and the tangent of b.

25.0 m

20.0 m

q

15.O m

y/x

tan q

x/y

tan b

tan q 20.0 m/ 15.0 m

tan b 15.0 m/ 20.0 m

tan q 1.33 ...

tan b 0.750

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