Trig Functions of Any Angle

Multiple Choice

We have just studied "Special Triangles": Is this triangle a 30-60-90 triangle?

• Yes, because it's a right triangle.

• Naw Dawg

Multiple Choice

Is this a 30-60-90 triangle?

• Like... totally!

• No.

• I don't know because I can't see any angle measures besides the right angle.

That is how Trigonometry Functions work!

Notice you are connecting a relationship of two side measures to an angle measure.

Because not all right triangles have an obvious "short leg"

(For example a 45-45-90)

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We need slightly different names.

Sine is the relationship between an acute angle in a right triangle and...

The ratio of the opposite and hypotenuse sides.

Cosine is the relationship between an acute angle in a right triangle and...

The ratio of the adjacent and hypotenuse sides.

Tangent is the relationship between an acute angle in a right triangle and...

The ratio of the opposite and adjacent sides.

I stubbed my toe on outdoor school and had to soak it in the river.

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< Memorize This

Multiple Choice

What is the Sin of 53.13 degrees?

• 4/5

• 3/4

• 3/5

• Yo no se.

Multiple Choice

What is the Cos of 53.13 degrees?

• 4/5

• 3/4

• 3/5

• Yo no se.

Multiple Choice

What is the Tan of 53.13 degrees?

• 4/5

• 4/3

• 3/5

• Yo no se.

Well, if you are standing on the 25 degree angle what is the side called that is marked 8m?

​

How do we use a calculator to find b and c?

The 8m side is "adjacent" to the 25 degree angle, so you must use a trig function with "adjacent" in the ratio.

Hint: SOH CAH TOA

Multiple Choice

Which Trig functions have "Adjacent" in the output?

• None of them?

• Only Cosine and Tangent

• All of them do.

• Only Sine and Cosine

Multiple Choice

Which Trig functions have "Hypotenuse" in the output ratio?

• None of them?

• Only Cosine and Tangent

• All of them do.

• Only Sine and Cosine

Multiple Choice

Which Trig functions does NOT need the hypotenuse?

• TAN

• SIN

• COS

• SOH CAH TOA

Multiple Choice

Which Trig functions does NOT need the adjacent side?

• TAN

• SIN

• COS

• SOH CAH TOA

Multiple Choice

Which Trig functions does NOT need the opposite side?

• TAN

• SIN

• COS

• SOH CAH TOA

Multiple Choice

If you are hiking to a glacier in Montana and you stub your toe, what should you do?

• TAN

• SIN

• COS

• SOH CAH TOA

Set up a function and solve:


Tan25= b/8

(Multiply both sides by the denominator)


8*Tan25 = b


Hint: SOH CAH TOA