trig help.. half angles etc

[leesuh190]

I have a trig test tomorrow and once again, i have no idea what I'm doing ><
Please help me!

Find all solutions in the interval [0,2

): sec^2x-3tanx=5
is this what i'm supposed to do? (1/(cos^2x)-3(sinx/cosx) ?

Find all solutions in the interval [0,2

): 1/(4sinx)

Find all solutions in the interval [0,2

): cos2x+sinx=0
for this one^ I assumed that I'm supposed to cahnge it to 1-sin^2x+sinx=0 but I dont know where to go from there...

Find the exact value of tan 157 degrees and 30' . (157 degrees and 30' is half of 315 degrees)
for this one... i got -1 because i used the forumla tan2u=(2tanu)/(1-tan^2u) and subsituted tan with -1 which i found on the unit circle. but my answer was undefined >< i'm supposed to get negative square root of two + one

Given cosx= -3/7 and /2 < x < , find cos (x/2)

 

[galactus]

I have a trig test tomorrow and once again, i have no idea what I'm doing ><
Please help me!

Find all solutions in the interval [0,2

): sec^2x-3tanx=5
is this what i'm supposed to do? (1/(cos^2x)-3(sinx/cosx) ?

You could use the identity, \(\displaystyle tan^{2}(x)+1=sec^{2}(x)\)

And get: \(\displaystyle \L\\1+tan^{2}(x)-3tan(x)-5=0\)

Now, if you look close, you have a quadratic. Let u=tan(x) and solve.

[quote:rbttcigv]Find all solutions in the interval [0,2

): cos2x+sinx=0
for this one^ I assumed that I'm supposed to cahnge it to 1-sin^2x+sinx=0 but I dont know where to go from there...

[/quote:rbttcigv]

For this, same principle. Let \(\displaystyle cos(2x)=cos^{2}(x)-sin^{2}(x)\)

Then you have: \(\displaystyle cos^{2}(x)-sin^{2}(x)+sin(x)=0\)

But, \(\displaystyle cos^{2}(x)=1-sin^{2}(x)\)

\(\displaystyle \L\\1-sin^{2}(x)-sin^{2}(x)+sin(x)=0\)

Now, do the quadratic thing again by letting u=?.

 

[leesuh190]

thanks for helping! but i have a question. what do you mean by let u=tanx?

 

[skeeter]

sec²x - 3tanx = 5

1 + tan²x - 3tanx = 5

tan²x - 3tanx - 4 = 0

u² - 3u - 4 = 0

(u - 4)(u + 1) = 0

u = 4 ... u = -1

tanx = 4 ... tanx = -1

x = arctan(4), x = arctan(4) + pi ... x = 3pi/4, x = 7pi/4