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C3 Trig Help!

I got a question that goes

'Without using a calculator, find the exact value of tan 75o' (8)

Any help where to start?
Reply 1
Avatar for sonofdot
sonofdot
8
tan⁡75=tan⁡(45+30)\tan 75 = \tan (45+30)

Do you know the formula for tan⁡(A±B)\tan (A \pm B)? :smile:
Reply 2
Avatar for sonofdot
sonofdot
8
You should know (from set square triangles) the values of tan30 and tan45
Reply 3
Avatar for Josh2802
Josh2802
OP
tan A + tan B
_____________
1 - tanAtanB = right?
so i put tan 45 for Tan A, and tan 30 for tan B?
Reply 4
Avatar for sonofdot
sonofdot
8
Josh2802
tan A + tan B
_____________
1 - tanAtanB = right?
so i put tan 45 for Tan A, and tan 30 for tan B?


Correct, then simplify :smile:
Reply 5
Avatar for Josh2802
Josh2802
OP
sonofdot
You should know (from set square triangles) the values of tan30 and tan45


Never heard 'set square triangles' but I know tan 45 is 1 and tan 30 is root 3/3
Reply 6
Avatar for sonofdot
sonofdot
8
Josh2802
Never heard 'set square triangles' but I know tan 45 is 1 and tan 30 is root 3/3


They're basically just two right angled triangles with angles (90, 30, 60) and (90, 45, 45), which give you the simple trig values - useful if you forget the value of, say, tan 45
Reply 7
Avatar for Josh2802
Josh2802
OP
sonofdot
Correct, then simplify :smile:


so on top line i get 1 + root3/3
bottom line 1 - 1xroot3 over 3? - basically 1 -root3/3?

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