Trig
posted by Kasey on .
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 = 180110=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
405360
Answer is 45°

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

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 rightangled 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