The question is like this:
Find sinx (without using a calculator) if you know that tanx=-2*(sqrroot)2.
90
-
Find sinx (without using a calculator) if you know that tanx=-2*(sqrroot)2.
90
-
We know that sin^2 x + cos^2 x = 1 for any angle x. Assuming cosx =/= 0, we divide by cos^2 x to get:
tg^2 x + 1 = 1/cos^2 x
since tg x = -2 sqrt2, we have tg^2 x = 8, so:
1/cos^2 x = 8 + 1 = 9, or:
cos^2 x = 1/9
Then: sin^2 x = 1 - cos^2 x = 1 - 1/9 = 8/9
We will take the square root of this, but first let's see what sign sinx should have: since 90 < x < 180, we know sinx should be positive. We can now take the square root, using the positive value as an answer:
sinx = (2 sqrt2)/3
tg^2 x + 1 = 1/cos^2 x
since tg x = -2 sqrt2, we have tg^2 x = 8, so:
1/cos^2 x = 8 + 1 = 9, or:
cos^2 x = 1/9
Then: sin^2 x = 1 - cos^2 x = 1 - 1/9 = 8/9
We will take the square root of this, but first let's see what sign sinx should have: since 90 < x < 180, we know sinx should be positive. We can now take the square root, using the positive value as an answer:
sinx = (2 sqrt2)/3
1
keywords: maths,Trig,problem,help,need,with,I need help with a Trig problem (maths)