Thread: Trig help pls :(

I need to solve the following for 0degrees<and equal to x <equal to 360

1) tan x=1 which i did tan^-1=45 +180=225

but i have others such as cos x=0.5 , cos x=-0.9 but i dnt know what to do!

Also without a calculator how can i show that sin60cos30+cos60sin30=1?

Thank you

Hello,

sin60cos30+cos60sin30=1?

We know that sin(a+b)=sin(a)cos(b)+sin(b)cos(a)

So here a=60, b=30

Thus what does sin(60+30) equal to ?
You can also remember that sin(60)=sqrt(3)/2, cos(30)=sqrt(3)/2, cos(60)=1/2 sin(30)=1/2

Originally Posted by Chez_

I[COLOR="DarkRed"] [snip]
cos x=0.5 , cos x=-0.9 but i dnt know what to do!

[snip]

You have to know all the special angles and their exact values ....

cos x = 0.5 => the reference angle is x = 60 degrees.

Therefore x = 60 + 360 n or x = 120 + 360n where n is an integer.


$\displaystyle \cos x= -0.9 => x = \cos^{-1} (-0.9)$. There's no special angle here so you have to get the reference angle using a calculator:

x = 154.2 degrees (correct to 1 decimal place).

Therefore x = 154.2 + 360 n or x = [(180 - 154.2) + 180] + 360n = 205.8 + 360n where n is an integer.


In both cases values of n are chosen to give solutions that lie inside the given solution domain.