Unit 3.4 Trigonometry

What is trigonometry?

Branch of math that deals with relationships between the sides and angles of triangles

The Pythagorean Theorem can be used when?

To determine missing side lengths of right triangles

A right triangle must contain what?

A 90^o angle

In a right triangle, what is special about the side opposite the 90^o angle?

It is always the longest side

The longest side of a right triangle is called what?

The hypotenuse

What is the formula for finding missing sides in a right triangle?

a² + b² = c²

What does “c” represent in a² + b² = c²?

“c” is always the hypotenuse

In order to use Pythagorean Theorem, what two things MUST we have to proceed?

Must have the lengths of 2 sides (cannot use it if you only have one side)

“Trigonometry is used to solve problems-”

“-regarding unknown sides or angles in triangles”

“The primary trigonometric ratios apply specifically to-”

“-right triangles”

A right triangle has a 90^o angle and what else?

Two acute angles

What is an acute angle?

An angle that is less than 90^o

When considering trigonometry, what mode does your calculator have to be in?

DEG or degree mode

The side beside an angle that isn’t the hypotenuse is called what?

The adjacent side

Besides the hypotenuse and the adjacent side, what the last side called?

Opposite

What does SOH CAH TOA mean?

• Sine is equal to Opposite divided by Hypotenuse

• Cosine is equal to Adjacent divided by Hypotenuse

• Tangent is equal to Opposite divided by Adjacent

E.g. SOH CAH TOA for angle C

When using Sine, Cosine, and Tangent, during the equations how many decimal places should you keep?

Keep 4

Define angle of elevation and angle of depression

• Angle of elevation is an angle above a horizontal reference line

• Angle of depression is an angle below a horizontal reference line

When searching for a missing angle when you have two sides, how do you use SOH, CAH, TOA?

The same way except you use sin^-1, cos^-1, tan^-1

What is an obtuse angle?

An angle that is greater than 90^o AND lesser than 180^o

What does the sum of all three angles in a triangle always equal?

180

Can a right triangle ever have an obtuse angle?

No

When working with obtuse angles, can we use SOH, CAH, TOA?

No

Define supplementary angles?

When two angles form a straight line together their sum is 180^o and thus they are supplementary to each other

What is the pattern (sign) for the sine of an obtuse angle?

The sine of an obtuse angle is positive

What is the pattern (sign) for the cosine of an obtuse angle?

The cosine of an obtuse angle is negative

What is the pattern (sign) for the tangent of an obtuse angle?

The tangent of an obtuse angle is negative

All acute angles will have positive or negative trig ratios?

Positive

Do obtuse angles have positive or negative trig ratios?

• Sine is always positive

• Cosine and Tangent are always negative

If using Sine/Cosine/Tangent and your answer has to be between 0^o and 180^o and you get a negative number, what do you do?

• Use its supplementary angle

• If the answer you got was -56^o then the proper answer is 124^o

An oblique triangle doesn’t have what?

Doesn’t have a right angle

If an oblique triangle doesn’t have a right angle, what else does it also not have?

It does not have a hypotenuse

What 2 methods can we use to solve for oblique triangles?

• Sine Law

• Cosine Law

What is the sine law equation?

What do lowercase letters and uppercase letters represent?

• Lowercase letters are the side lengths

• Uppercase letters are the corresponding angles (in degrees)

When given a problem, look right away for a 90^o angle. Why?

• If a 90^o angle is present you can use SOH, CAH, TOA

• Without a 90^o angle you can’t ☹

What is a trick if you have 2 angles and only missing one?

• Subtract the known angles from 180

• Remember that a triangle’s three angles will always equal 180

TO SUM WHAT WE’VE LEARNED SO FAR how do you solve for right triangles and how do you solve for oblique triangles?

• Right = SOH CAH TOA

• Oblique = Sine Law (BUT only if we have or can find a matching angle/side pair)

When given an oblique triangle without a corresponding angle/side pair, what method can you use if not Sine Law?

Cosine Law

The Cosine Law is derives from what?

Pythagorean Theorem

What is the formula for Cosine Law?

What important thing do you have to remember about an equation like this:

a = b - 2c

If you divide both sides by b, the right side will be left with negative 2c

In what situations should you use Sine Law?

• When you have a side-angle pair meaning you have and angle and it’s opposite length and one other piece of information

• Know 2 angles and any side and need to find a side

• Know 2 sides and an angle that is not between them and need to find an angle

In what situations should you use Cosine Law?

• Do not have any complete side-angle pairs

• Know all three sides and need to find an angle

• Know two sides and the angle trapped between them