**TRIGONOMETRIC RATIOS OF ACUTE ANGLES**

Example 1:

Find the value of

with the calculator rounded to four decimal places. The calculator must be in degree mode!sin 34^{o}Input:

sin(34)ENTERNOTE: 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}0.5592Please note that the value of

is an irrational number. That is, it has an infinite number of decimal places!sin 34^{o}

Example 2:

Find the value of

with the calculator rounded to four decimal places. The calculator must be in degree mode!cos 75^{o}Input:

cos(75) ENTER

cos 75^{o}0.2588Please note that the value of

is an irrational number. That is, it has an infinite number of decimal places!cos 75^{o}

Example 3:

Find the value of

with the calculator rounded to four decimal places. The calculator must be in degree mode!tan 84^{o}Input:

tan(84)ENTERNOTE: 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.Please note that the value of

tan 84^{o}9.5144is an irrational number. That is, it has an infinite number of decimal places!tan 84^{o}

Example 4:

Find the value of

with the calculator rounded to three decimal places.csc 39^{o}

Calculators only have a sin, cos, and tan key.Therefore, we MUST know and use theReciprocal Identity.We also must make sure that the calculator is in degree mode.

Input:

1sin(39) ENTER

csc 39^{o}1.589Please note that the value of

is an irrational number. That is, it has an infinite number of decimal places!csc 39^{o}

Example 5:

Find the value of

sec 13with the calculator rounded to three decimal places.^{o}

We MUST use theReciprocal Identity.We also must make sure that the calculator is in degree mode.

Input:

1cos(13) ENTER

sec 13^{o}1.026Please note that the value of

sec 13is an irrational number. That is, it has an infinite number of decimal places!^{o}

Example 6:

Find the value of

with the calculator rounded to three decimal places.cot 64^{o}We can use the

Reciprocal Identityor theQuotient Identity.

NOTE: When working with the calculator, it is always best to use theQuotient Identitywhen evaluating cotangent. Sometimes, the calculator gives incorrect results when theReciprocal Identityis used.We must make sure that the calculator is in degree mode.

Input:

cos(64)sin(64) ENTER

cot 64^{o}0.488Please note that the value of

is an irrational number. That is, it has an infinite number of decimal places!cot 64^{o}

Example 7:

Use the calculator to find the value of

rounded to 3 decimal places.tan 1Since 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 1.557Please note that the value of

is an irrational number. That is, it has an infinite number of decimal places!tan 1

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 thesymbol 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

rounded to three decimal places.sec 1.4Since there is no degree symbol attached to the angle, the calculator must be in radian mode!

We MUST use the

Reciprocal Identity.Input:

1cos (1.4) ENTER

sec 1.4 5.883Please note that the value of

is an irrational number. That is, it has an infinite number of decimal places!sec 1.4

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 ) ENTERPlease 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

. Use a calculuator to find it.sin 60^{o}The calculator must be in degree mode!

Input:

sin(60)ENTER

and we memorized that given the sepcial anglesin 60^{o}0.866.60^{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

modebutton and observe the modesorCLASSICin the last row of the display window. Use the arrow buttons (located under the display window) to highlight theMATHPRINTmode. PressMATHPRINTenterand thenclear.

Example 12:

Assume you forgot the EXACT value of

. Use a calculuator to find it.sin 45^{o}The calculator must be in degree mode!

Input:

sin (45) ENTER

sin 45^{o}^{ }and we memorized that given the special angle0.707.45^{o}

Example 13:

Assume you forgot the EXACT value of

. Use a calculuator to find it.tan 60^{o}The calculator must be in degree mode!

Input:

tan (60) ENTER

tan 60^{o}and we memorized that given the special angle1.732.60^{o}

Example 14:

Assume you forgot the EXACT value of

. Use a calculuator to find it.tan 30^{o}The calculator must be in degree mode!

Input:

tan (30) ENTER

tan 30^{o}and we memorized that given the special angle0.577.30^{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) ENTERAlways use thesymbol on the calculator and not 3.14.and we memorized that given the special angle

().30^{o}