# 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

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

• 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.

#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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