Six Trigonometric Ratios

Six

Trigonometric

Ratios

By Loreno Norcio

Objectives

By the end of the lesson, you are expected to

• identify parts of a Right Triangle

• illustrate the six trigonometric ratios: sine, cosine, tangent, secant, cosecant, and cotangent

• value the uses of trigonometric ratios

Six Trigonometric Ratios

Activity 1:

Right Triangle is Right

Draw

Name the sides of the right triangle.

Activity 2:

The Sides

Fill in the Blank

Observe the given figure. Look at angle X and complete the statement below.

"The OPPOSITE SIDE is found ________ angle X."

Fill in the Blank

Observe the given figure. Look at angle X and complete the statement below.

"The ADJACENT SIDE is found ________ angle X."

Fill in the Blank

Observe the given figure. Look at right angle and complete the statement below.

"The HYPOTENUSE SIDE is found opposite the _____ angle."

Activity 3:

The Trio

Loreno Norcio

Multiple Choice

The SINE (sin) of an angle $$\theta$$  is the ratio of the opposite side to the hypotenuse. Which is its mathematical representation?

• $$\sin\theta=\frac{opposite}{hypotenuse}$$  

• $$\sin\theta=\frac{hypotenuse}{opposite}$$  

Multiple Choice

The COSINE (cos) of an angle $$\theta$$  is the ratio of the adjacent side to the hypotenuse. Which is its mathematical representation?

• $$\cos\theta=\frac{hypotenuse}{adjacent}$$  

• $$\cos\theta=\frac{adjacent}{hypotenuse}$$  

Multiple Select

The TANGENT (tan) of an angle $$\theta$$  is the ratio of the sine to cosine. Which is its mathematical representation?

• $$\tan\theta=\frac{\sin\ \theta}{\cos\ \theta}$$  

• $$\tan\theta=\frac{opposite}{adjacent}$$  

​Activity 4:

The Other Three

Loreno Norcio

Multiple Choice

The COSECANT (csc) of an angle $$\theta$$  is the reciprocal of SINE. Which is its mathematical representation?

• $$\csc\theta=\frac{hypotenuse}{opposite}$$  

• $$\csc\theta=\frac{opposite}{hypotenuse}$$  

Multiple Choice

The SECANT (sec) of an angle $$\theta$$  is the reciprocal of COSINE. Which is its mathematical representation?

• $$\sec\theta=\frac{adjacent}{hypotenuse}$$  

• $$\sec\theta=\frac{hypotenuse}{adjacent}$$  

Multiple Choice

The COTANGENT (cot) of an angle $$\theta$$  is the reciprocal of TANGENT. Which is its mathematical representation?

• $$\cot\theta=\frac{opposite}{adjacent}$$  

• $$\cot\theta=\frac{adjacent}{opposite}$$  

MNEMONICS

​SOH-CAH-TOA

​

CscHO-SecHA-CotAO​

​Activity 5

Applications of Trigonometric Ratios

Loreno Norcio

Draw

Identify the applications of trigonometric ratios based on the following pictures.

Draw

Identify the applications of trigonometric ratios based on the following pictures.

Draw

Identify the applications of trigonometric ratios based on the following pictures.