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In Exercises 9-16,

use the given triangles to evaluate each
expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

In Exercises 9-16, use the given triangles to evaluate each expression. If necessary-example-1
User Jeahel
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The values of the trigonometric ratios are:

9) √3/2

10) √3/3

11) √2

12) √2

13) √3

14) √3/3

15) 0

16) 3

What is trigonometric ratios?

Trigonometric ratios relate the sides of a right triangle: sine, cosine, tangent, cosecant, secant, and cotangent. They express geometric relationships.

Using trigonometric ratios of standard special angles.

9) Cos30 = √3/2

10) Tan30 = 1/√3

Rationalize

√3/3

11) Sec45 = 1/cos45

= √2

12) Csc45 = 1/sin45

= √2

13) tan(π/3) = tan60

π radians = 180⁰

tan60 = √3

14) cot(π/3) = cot60

cot = 1/tan60

= 1/√3

Rationalize

= √3/√3*√3 = √3/3

15) sin(π/4) - cos(π/4)

= sin45 - cos45

=1/√2 - 1/√2 = 0

16) tan(π/4) + csc(π/6)

tan45 + csc30

tan45 + 1/sin30

= 1 + 2

= 3

User Steven Johnston
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