HW 68: Trig Ratio Worksheet Answer Key The trig. ratios, sine, cosine, and tangent are based on properties of right triangles. The function values depend on the measure of the angle. sine θ = sin θ = (side opposite θ)/hypotenuse cosine θ = cos θ = (side adjacent θ)/hypotenuse tangent θ = tan θ = (side opposite θ)/(side adjacent θ) In triangle ABC, sin A = a/c, cos A = b/c, and tan A = a/b.

Calculate the trig ratios based on the pictures below:

1) sin Y = 5 3 3

10 2 7) sin R =

4

5

2) cos Y = 5 1

10 2 8) cos R =

3

5

3) tan Y = 5 3

35

9) tan R = 4

3

4) sin Z = 5 1

10 2 10) sin Q =

3

5

5) cos Z =5 3 3

10 2 11) cos Q =

4

5

6) tan Z =5 3

35 3 12) tan Q =

3

4

Convert the following fractions to decimals, rounding your answer to the ten-thousandths place:

13) 5

10= .5000 14)

5 3

10= ..8660 15)

5 3

5= 1.7321

Convert the following to decimals. Do not round! Leave answers precise, but in decimal form.

16) 4

5= .8 17)

3

5= .6 18)

4

3= 1.3

Use your calculator to find the inverse sine, “sin-1“ (2nd then SIN on most calculators) of the values above. Write the results here:

13) 30 14) 60 15) ERROR 16) 53.13 17) 38.87 18) ERROR

adjacent

10

5

5 3

X Y

Z

5

3

4

P R

Q

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