Trig

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Can someone check my answers so far?

1. Find the exact value of tan(-3ð)

Answer: tan(-3ð) = tan (-3 + 2ð) = tan (-ð) = tan (-ð + 2ð) = tan(ð) = sin (ð)/cos(ð) = (0)/(-1) = 0

Exact value is 0


2. Solve triangleABC is C = 90 degrees, B = 20 degrees, and b = 10. Round the measures of sides to the nearest tenth and measure angles to the nearest degree.

Work:
(sinA)/a = (sinB)/b = (sinC)/c

(sin90)/c = (sin20)/10 = 1/c = 0.34/10

A+20+90=180 A = 180-110=70

(sinA)/9 = (sinB)/b

(sin70)/9 = (sin20)/10

0.93/9 = 0/34/10

0.93 * 0.034 = a = 27.35 -> 27.4

Answer is:
A= 70, B= 20, C=90
a=27.4 b=10, c=29.4


3. Find the exact value of sin405degrees

Work:
sin405°=sin45=+0.70711
405-360

Answer is 45°

  • Trig -

    the ð is suppose to be the pi symbol. it didn't work when i posted it!

  • Trig -

    in #1, why not add 4pi ?
    tan(-3pi) = tan(-3pi + 4pi) = tan(pi)
    etc.
    your answer is correct


    #2.

    I don't see where the 9 came from in sin70 /9.
    Since you have a right-angled triangle there is no need to use the Sine Law, just do..
    tan 70 a/10
    a = 27.4 (you had that)

    and

    cos 70 = 10/c
    c = 10/cos70 = 29.23

    you could have found c by Pythagoras
    c^2 = 10^2 = 27.47477^2 = 29.23

    #3 you did not finish

    sin 405º
    = sin 45º
    = 1/√2 or √2/2

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