trigonometric identities

Intro to Trigonometry: Tangent, Cosine, and Sine

Opposite, Adjacent, and Hypotenuse

In order to use any trigonometric identity, you must first understand how to find the opposite side, adjacent side, or hypotenuse for any given angle.

Side AB is opposite of the right angle. Whichever side is opposite of the right angle is always the Hypotenuse.

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Angle A is adjacent to side AC and opposite to side BC

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Angle B is adjacent to side BC and opposite to side AC

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Angle C doesn't count for trig identities

Consider the following...

Multiple Choice

Which side is adjacent to <A?

• x

• y

• z

Multiple Choice

Which side is opposite to <A?

• x

• y

• z

Multiple Choice

Which side is adjacent to <B?

• x

• y

• z

Multiple Choice

Which side is the hypotenuse?

• x

• y

• z

Soak your toes!

I mean...

SOH-CAH-TOA

^remember that instead of constantly referring back to the formula charts!​

tan(gent), cos(ine), sin(e)

The Tangent ratio for either of the non-right angles in a right triangle is the length of the opposite side divided by the length of the adjacent side.

The Tangent Formula

Multiple Choice

The Tangent of angle A is ____.

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$  

Multiple Choice

$$Tan\left(B\right)=$$  

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$  

The Cosine ratio for either of the non-right angles in a right triangle is the length of the adjacent side divided by the length of the hypotenuse.

The Cosine Formula

Multiple Choice

The Cosine of angle A is ____.

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$  

Multiple Choice

$$Cos\left(B\right)=$$  

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$  

The Sine ratio for either of the non-right angles in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

The Sine Formula

Multiple Choice

The Sine of angle A is ____.

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$  

Multiple Choice

$$Sin\left(B\right)=$$  

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$