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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 Blanks

Fill in the Blanks

Fill in the Blanks

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​

Multiple Choice

Give the ratio for $\tan\theta$  

•  $\frac{adjacent}{opposite}$  

•  $\frac{opposite}{adjacent}$  

•  $\frac{adjacent}{hypotenuse}$  

•  $\frac{opposite}{hypotenuse}$  

Multiple Choice

Give the ratio for  $\cos\theta$  

•  $\frac{adjacent}{hypotenuse}$  

•  $\frac{opposite}{adjacent}$  

•  $\frac{adjacent}{opposite}$  

•  $\frac{opposite}{hypotenuse}$  

Multiple Choice

cos 87

• .05
• .569
• .0523
• .5700

Multiple Choice

What is the correct ratio?

• $\frac{6}{10}$

• $\frac{6}{8}$

• $\frac{8}{10}$

• $\frac{8}{6}$

Multiple Choice

What is the length of the hypotenuse side?

• 8

• 15

• 17

Multiple Choice

Choose the correct ratio.

• $\sin\ Z=\frac{5}{13}$

• $\sin\ X=\frac{5}{13}$

• $\cos\ X=\frac{12}{13}$

• $\tan\ Z=\frac{12}{5}$

Multiple Choice

What is the correct ratio for tan A?

• $\frac{20}{12}$

• $\frac{12}{20}$

• $\frac{12}{16}$

• $\frac{16}{12}$

Multiple Choice

What is the formula for secant?

• $\sec=\frac{adjacent}{opposite}$

• $\sec=\frac{hypotenuse}{opposite}$

• $\sec=\frac{opposite}{hypotenuse}$

• $\sec=\frac{hypotenuse}{adjacent}$

Multiple Choice

What is the formula for cosecant?

•  $\csc=\frac{adjacent}{opposite}$  

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

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

•  $\csc=\frac{hypotenuse}{adjacent}$  

Multiple Choice

what is the formula for cotangent

• $\cot=\frac{adjacent}{opposite}$

• $\cot=\frac{hypotenuse}{opposite}$

• $\cot=\frac{opposite}{hypotenuse}$

• $\cot=\frac{hypotenuse}{adjacent}$

Multiple Choice

Identify side XZ, with respect to the marked angle.

• altitude

• hypotenuse

• opposite

• adjacent

Multiple Choice

Identify side LN, with respect to the marked angle.

• altitude

• hypotenuse

• opposite

• adjacent

Multiple Choice

Identify the mnemonic used with trigonometric ratios.

• SAH COA TOH

• SOA CAH TOA

• SHO CAH THA

• SOH CAH TOA

Multiple Choice

Identify the trigonometric ratio that may be used to find the marked unknown angle.

•  $\sin\ y\degree=\frac{12}{18}$  

•  $\cos\ y\degree\ =\ \frac{18}{12}$ 

•  $\cos\ y\degree\ =\ \frac{12}{18}$ 

•  $\tan\ y\degree=\ \frac{12}{18}$ 

Multiple Choice

The reciprocal of sine is the ...

• Secant

• Cosecant

• Cotangent

• Cosine

Multiple Choice

The reciprocal of cosine is the ...

• Secant

• Cotangent

• Sine

• Cosecant

Multiple Choice

The reciprocal of tangent is the ...

• Secant

• Cotangent

• Cosine

• Cosecant

Multiple Choice

Which trigonometric ratio is correct?

• $\sin\ A=\frac{opposite}{adjacent}$

• $\cos\ A=\frac{opposite}{hypotenuse}$

• $\tan\ A=\frac{opposite}{adjacent}$

• $\sin\ A=\frac{adjacent}{opposite}$

Multiple Choice

Give the ratio for  $\sin\theta$  

•  $\frac{adjacent}{hypotenuse}$  

•  $\frac{opposite}{adjacent}$  

•  $\frac{adjacent}{opposite}$  

•  $\frac{opposite}{hypotenuse}$  

Multiple Choice

Q: What is the correct ratio?

• $$\frac{6}{10}$$

• $$\frac{8}{10}$$

• $$\frac{6}{8}$$

• $$\frac{8}{6}$$

Multiple Choice

What type of triangle is the context of our study of trigonometry and Pythagorean Theorem?

• right triangle

• isosceles triangle

• scalene triangle

• acute triangle

Multiple Choice

Which trigonometric function does not use the hypotenuse in its ratio?

• sine

• cosine

• tangent

• secant

Multiple Choice

Find the ratio for cos A. Simplify the fraction.

• 36/27

• 3/5

• 36/45

• 4/5

Multiple Choice

What is the reciprocal of sine?

• cosine

• secant

• sin ^-1

• cosecant

Multiple Choice

Find sin A.

• 7/25

• 24/7

• 24/25

• 7/24

Multiple Choice

Find sin D.

• 12/13

• 5/13

• 13/5

• 13/12

Multiple Choice

Find tan B.

• 7/25

• 24/7

• 24/25

• 7/24

Multiple Choice

Which side is opposite to angle A?

• AC

• BC

• AB

Multiple Choice

Which side is opposite to angle D?

• DF

• ED

• EF

Multiple Choice

What is the ratio for cosine?

• opposite/hypotenuse

• adjacent/hypotenuse

• opposite/adjacent

• hypotenuse/adjacent