Algebra 1 Common Core Student Edition, Grade 8-9

Pl an
How do you calculate
trigonometric ratios?
Calculate a trigonometric
ratio by substituting
the lengths of the
appropriate sides into
the ratio.

What are sin A, cos A, and tan A for the triangle shown?

opposite leg _ 15

Fi n d i n g Tr i g o n o m et r i c Rat i o s

sinyl =

cos ,4 =

tan A =

hypotenuse

ad jacent leg

hypotenuse

opposite leg

ad jacent leg

17

JL

' 17

15

8

Go t i t? 1. W hat are sin E, cos E, and tan E for th e triangle below?

F

You can also use a calculator to find trigonom etric ratios. In this chapter, use Degree

m ode w h en finding trigonom etric ratios. That allows you to en ter angles in degrees.

Sci Eng

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Radian BKBHSEi

Pol Seq

Dot

Simul

a + b i r e A 0i

Driz G-T

Set your calculator

to Degree mode.

rhm k

What is an upper

limit on the value of

the cosine?

The cosine is the ratio

adjacent leg...

h^=lnar'9ht

triangle. The hypotenuse

is always the longest

side. The cosine of an

acute angle is always less

than 1.

Finding a Trigonometric Ratio

What is the value of cos 55° to the nearest ten-thousandth?

To find cos 55°, press 55.

The cosine of 55° is approxim ately 0.5736.

6RIDDED RESPONSE

© Got It? 2. W hat is the value of each expression in p arts (a)-(d)?

a. sin 80° b. ta n 45° c. cos 15° d. sin 9°

e. Reasoning D escribe th e relationship betw een sin 45° an d cos 45°.

Explain why this is true.

646 Chapter 10 Radical Expressions and Eq uat io ns