im stuck :(

[beezy4eva]

i think this questions supposed to be easy but ive just had a total mental blank:
if tan(x)= 1/4 where  π ≤ x ≤ 3π/2 find the exact values of:
a) sin(x)     b)cos(x)

help would be much appreciated

[dcc]

now imagine a right angled triangle, we know that:




So you know that the two non-hypotenuse sides of the right-angled triangle are side lengths 1 & 4.

Using Pythag, you can find the length of the remaining side





So to find sin(x), remember that sin(x) = opposite/hypotenuse


BUT since we know that , then sin(x) will be negative (because x is in the third quadrant, where only tan is positive)

so
(rationalising the denominater)

cos(x) is very much the same, but using cos(x) = adjacent / hypotenuse

edit: my gay teachers told us what appears to be the fourth quadrant is the first! dumb teacher!

[beezy4eva]

thanks

[Collin Li]

That is the alternative method. The conventional method is:

(dividing both sides by )

Substituting into yields:




Since (quadrant 3), then .


Now, using , we can find .

Note that this method is equivalent to the method described above, and the method above (by dcc) is more efficient for this type of question, but this is how you use the trigonometric identities to solve it.

[dcc]

if they gave you something like sin(x) = 0.2222212332340829342835072342430 then you'd have to do it using a trig identity rather then with triangles