**Trig for Beginners**

**A simple guide to learning the basics of trigonometry**

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5.Solving word problems in trigonometry:

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Have you started to learn about trigonometry? Confused? Looking for a source to gain an easier understanding? Well look no further my friend!

Trig for Beginners

will grant you the basic knowledge of the relations between the elements of a triangle!

Sine

Cosine

Tangent

Also know as sin, cos and tan for short.

The Right Angle Triangle

The longest side is called the

HYPOTENUSE

.

The side opposite to angle is called the

OPPOSITE.

The side next to angle (but is not the hypotenuse) is called the

ADJACENT.

θ

θ

Θ

On a right angle triangle, there are names for each side.

Now it's your turn to practice!

(Answers provided)

Answers:

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Answer:

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Answer:

1.

The three main functions in trigonometry:

These core functions specify the ratio of certain sides!

Why didn't Tan and Sin do their math homework?

Just 'cos!

To calculate sin, cos, and tan, you have to divide one side of the triangle by another.

The easiest way to remember which sides to use is by memorizing the word

SOHCAHTOA.

S

O

H

C

A

H

T

O

A

S

in =

o

pposite /

h

ypotenuse

C

os =

a

djacent /

h

ypotenuse

T

an =

o

pposite /

a

djacent

Many good calculators have sin, cos and tan buttons, You just have to punch in the angle then press the button.

Find sin , cos , and tan , for both triangles, expressed as fractions in lowest terms.

a)

b)

12m

8m

8.9m

a) Sin = opp Cos = adj Tan = opp

hyp hyp adj

= 3 = 4 = 3

5 5 4

b) Sin = opp Cos = adj Tan = opp

hyp hyp adj

= 89 = 2 = 89

120 3 80

Using your calculator, evaluate each of the following, rounding to three decimal places.

a) sin 46

b) cos 23.7

c) tan 79

d) cos 0

a) 0.902

b) 0.138

c) 0.496

d) 1

What is cos of angle ?

SOH

CAH

TOA

cos = adj over hyp

adj = 6

hyp = 10

Therefore cos = 6 or 3

10 5

Congratulations! Hopefully by now you have a better understanding of trigonometry! The key to success will be to constantly practice different problems and ask your teacher if you have any questions. Practice makes perfect!

There are of course, other less common functions.

Secant Function = hypotenuse / adjacent

This is the inverse of cosine.

Cosecant Function = hypotenuse / opposite

This is the inverse of sine.

Cotangent Function = ajacent / opposite

This is the inverse of tangent.

So basically, they are the opposite of the 3 core functions.

When you are using your calculator to find these, all you do is press "second function" then type in the angle, then sin / cos / tan.

When solving word problems in geometry, two terms will appear often:

Angle of elevation and angle of depression.

The angle of elevation is

always

inside the triangle, and measured from the ground up. So think of it as you having to elevate your eyes to see the top of the tree.

The angle of depression is

always

outside the triangle. This time, think of it as you having to lower (or depress) your eye level to see the boat.

ANGLE OF ELEVATION = ANGLE OF DEPRESSION

As you can see, side CA of the angle of elevation diagram is parallel to the horizon line in the angle of elevation diagram. These are called alternate interior angles. and therefore...

Knowing the Sum of angles in a triangle theorem, you can use the provided information to figure out the answer to the word problem! The triangle's interior angle must add up to 180 degrees, and we already know one angle is 90 degrees. Therefore, the two remaining angles must add up to 90 degrees, but one of them has to add up to a

different

90 degrees with the angle of depression! The answer is 55 degrees and 35 degrees!

A ladder that is 5 m long, leaning against a vertical wall makes an angle of 65˚ with the ground.

a) How high on the wall does the ladder reach?

b) How far is the foot of the ladder from the wall?

c) What angle does the ladder make with the wall?

a) The height that the ladder reaches is the side PQ.

PQ = sin 65˚ × 5 = 4.53 m

Therefore the height of the ladder is 4.53m.

b)The distance of the foot of the ladder from the wall is RQ.

RQ = cos 65˚ × 5 = 2.11 m

Therefore the ladder is 2.11m from the wall.

c) The angle that the ladder makes with the wall is angle P

Therefore the angle that the ladder makes with the wall is 25 degrees.

If the distance of a person from a tower is 100 m and the angle subtended by the top of the tower with the ground is 30o, what is the height of the tower in meters?

AB = distance of the man from the tower = 100 m

BC = height of the tower = h (to be calculated)

The trigonometric function that uses AB and BC is tan A , where A = 30o.

So tan 30o = BC / AB = h / 100

Therefore height of the tower h = 100 tan 30o = (100) 1/√3 = 57.74 m.