Trig Question

**brian890** · December 2nd 2011, 02:33 PM

Find the values of sinx and tanx if cosx=4/5 and x is in the first quadrant.

**Quacky** · December 2nd 2011, 02:36 PM

Draw yourself a right triangle with an unnamed angle $\theta$ . We know the adjacent side is 4 units and the hypotenuse is 5 units.

**brian890** · December 2nd 2011, 02:40 PM

Okay, then I get sinx= 3/5 and tanx=3/4. Do I take the inverse of these to get my answer?

**Quacky** · December 2nd 2011, 02:56 PM

No, you're done. The question wanted you to find $sin(x)$ and $tan(x)$ , indeed the inverses are ghastly numbers.

**Archie Meade** · December 2nd 2011, 03:10 PM

Alternatively,

$Sin^2x+Cos^2x=1\Rightarrow\ Sin^2x=1-Cos^2x=1-\frac{16}{25}=\frac{25}{25}-\frac{16}{25}=\frac{9}{25}$

$\Rightarrow\ Sinx=\frac{3}{5}$

as Sin(x) is positive in the first quadrant.

$Tanx=\frac{Sinx}{Cosx}=\frac{3\left(\frac{1}{5} \right)}{4\left(\frac{1}{5} \right)}=\frac{3}{4}$

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