TRIGONOMETRIC RATIOS OF ACUTE ANGLES

Example 1:

Find the value of sin 34^o with the calculator rounded to four decimal places.  The calculator must be in degree mode!

Input: sin(34) ENTER

NOTE:  Left parenthesis will open when we activate the trigonometric function buttons on the calculator.  After we type in the angle also called the argument, we MUST type in the right parenthesis, namely ")", before we press ENTER.

sin 34^o 0.5592

Please note that the value of sin 34^o is an irrational number. That is, it has an infinite number of decimal places!

Example 2:

Find the value of cos 75^o with the calculator rounded to four decimal places. The calculator must be in degree mode!

Input: cos(75) ENTER

cos 75^o 0.2588

Please note that the value of cos 75^o is an irrational number. That is, it has an infinite number of decimal places!

Example 3:

Find the value of tan 84^o with the calculator rounded to four decimal places.  The calculator must be in degree mode!

Input: tan(84) ENTER

NOTE:  Left parenthesis will open when we activate the trigonometric function buttons on the calculator.  After we type in the angle also called the argument, we MUST type in the right parenthesis, namely ")", before we press ENTER.

tan 84^o 9.5144

Please note that the value of tan 84^o is an irrational number. That is, it has an infinite number of decimal places!

Example 4:

Find the value of csc 39^o with the calculator rounded to three decimal places.

Calculators only have a sin, cos, and tan key.  Therefore, we MUST know and use the Reciprocal Identity  . 

We also must make sure that the calculator is in degree mode.

Input: 1 sin(39) ENTER

csc 39^o 1.589

Please note that the value of csc 39^o is an irrational number. That is, it has an infinite number of decimal places!

Example 5:

Find the value of sec 13^o with the calculator rounded to three decimal places.
We MUST use the Reciprocal Identity . 

We also must make sure that the calculator is in degree mode. 

Input: 1 cos(13) ENTER

sec 13^o 1.026

Please note that the value of sec 13^o is an irrational number. That is, it has an infinite number of decimal places!

Example 6:

Find the value of cot 64^o with the calculator rounded to three decimal places.

We can use the Reciprocal Identity or the Quotient Identity . 

NOTE: When working with the calculator, it is always best to use the Quotient Identity when evaluating cotangent. Sometimes, the calculator gives incorrect results when the Reciprocal Identity is used.

We must make sure that the calculator is in degree mode. 

Input: cos(64) sin(64) ENTER

cot 64^o 0.488

Please note that the value of cot 64^o is an irrational number. That is, it has an infinite number of decimal places!

Example 7:

Use the calculator to find the value of tan 1 rounded to 3 decimal places. 

Since there is no degree symbol attached to the angle, the calculator must be in radian mode! Please note that radians are not always expressed in terms of .

Input: tan(1) ENTER 

tan 1 1.557

Please note that the value of tan 1 is an irrational number. That is, it has an infinite number of decimal places!

Example 8:

Use the calculator to find the value of rounded to three decimal places.

Since there is no degree symbol attached to the angle, the calculator must be in radian mode!

Input: cos(8) ENTER

NOTE: Always use the symbol on the calculator and not 3.14. 

Please note that the value of is an irrational number. That is, it has an infinite number of decimal places!

Example 9:

Use the calculator to find the value of sec 1.4 rounded to three decimal places.  

Since there is no degree symbol attached to the angle, the calculator must be in radian mode!

We MUST use the Reciprocal Identity . 

Input: 1 cos (1.4) ENTER

sec 1.4 5.883

Please note that the value of sec 1.4 is an irrational number. That is, it has an infinite number of decimal places!

Example 10:

Use the calculator to find the value of  rounded to three decimal places.  

Since there is no degree symbol attached to the angle, the calculator must be in radian mode!

We MUST use the Reciprocal Identity . 

Input: 1 (7 8 ) ENTER  

Please note that the value of is an irrational number. That is, it has an infinite number of decimal places!

Example 11:

Assume you forgot the EXACT value of sin 60^o. Use a calculuator to find it.

The calculator must be in degree mode!

Input: sin(60) ENTER

sin 60^o0.866 and we memorized that given the sepcial angle 60^o.

NOTE:

Some calculators have MATHPRINT. They display exact values of trigonometric ratios.

For example, if you have the TI-30XS Multiview Scientific Calculator, press the mode button and observe the modes CLASSIC or MATHPRINT in the last row of the display window. Use the arrow buttons (located under the display window) to highlight the MATHPRINT mode. Press enter and then clear.

Example 12:

Assume you forgot the EXACT value of sin 45^o. Use a calculuator to find it.

The calculator must be in degree mode!

Input: sin (45) ENTER

sin 45^o 0.707 and we memorized that given the special angle 45^o.

Example 13:

Assume you forgot the EXACT value of tan 60^o. Use a calculuator to find it.

The calculator must be in degree mode!

Input: tan (60) ENTER

tan 60^o 1.732 and we memorized that given the special angle 60^o.

Example 14:

Assume you forgot the EXACT value of tan 30^o. Use a calculuator to find it.

The calculator must be in degree mode!

Input: tan (30) ENTER

tan 30^o 0.577 and we memorized that given the special angle 30^o.

Example 15:

Assume you forgot the EXACT value of. Use a calculuator to find it.

There is no degree symbol attached to the angle, therefore, the calculator must be in radian mode!

Input: cos(6) ENTER      Always use the symbol on the calculator and not 3.14. 

and we memorized that given the special angle (30^o).