Few Trig Questions

May 2010
3
0
I need help with a few questions, if someone could do the problem and show how you did it that would be great.

Solve In Radians
2sinx -1 = o

sinx=squareroot of 3 - sinx

Angle Addition
Tan 105 degrees

Find each value of the trig function
Sin u = 3/5 cos u = 7/25


Thanks.
 

masters

MHF Helper
Jan 2008
2,550
1,187
Big Stone Gap, Virginia
I need help with a few questions, if someone could do the problem and show how you did it that would be great.

Solve In Radians
2sinx -1 = o

sinx=squareroot of 3 - sinx

Angle Addition
Tan 105 degrees

Find each value of the trig function
Sin u = 3/5 cos u = 7/25


Thanks.
Hi nyyfn26,

Here's a couple of them.

[1] \(\displaystyle 2 \sin x-1=0\)

\(\displaystyle 2 \sin x = 1\)

\(\displaystyle \sin x = \frac{1}{2}\)

\(\displaystyle x=\left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\}\) where \(\displaystyle 0 \leq x \leq 2 \pi\)

[2] \(\displaystyle \sin x = \sqrt{3}-\sin x\)

\(\displaystyle 2 \sin x=\sqrt{3}\)

\(\displaystyle \sin x = \frac{\sqrt{3}}{2}\)

\(\displaystyle x=\left\{\frac{\pi}{3}, \frac{2\pi}{3}\right\}\) where \(\displaystyle 0 \le x \le 2 \pi\)
 
May 2010
3
0
Hi nyyfn26,

Here's a couple of them.

[1] \(\displaystyle 2 \sin x-1=0\)

\(\displaystyle 2 \sin x = 1\)

\(\displaystyle \sin x = \frac{1}{2}\)

\(\displaystyle x=\left\{\frac{\pi}{6}, \frac{5\pi}{6}\right\}\) where \(\displaystyle 0 \leq x \leq 2 \pi\)

[2] \(\displaystyle \sin x = \sqrt{3}-\sin x\)

\(\displaystyle 2 \sin x=\sqrt{3}\)

\(\displaystyle \sin x = \frac{\sqrt{3}}{2}\)

\(\displaystyle x=\left\{\frac{\pi}{3}, \frac{2\pi}{3}\right\}\) where \(\displaystyle 0 \le x \le 2 \pi\)
Thank you.
 

masters

MHF Helper
Jan 2008
2,550
1,187
Big Stone Gap, Virginia
And another one,

[3] \(\displaystyle \tan 105 = \tan(60+45) = \frac{\tan 60+\tan 45}{1-\tan 60 \tan 45}=\frac{\sqrt{3}+1}{1-\sqrt{3}(1)}\)
 

masters

MHF Helper
Jan 2008
2,550
1,187
Big Stone Gap, Virginia
And the last one..... I think you mean to find the other trig ratios given the sine ratio of an angle, and given the cosine of another angle. Is that right?

[4] \(\displaystyle \sin u=\frac{3}{5}=\frac{y}{r}\)

Use Pythagoras to find x: \(\displaystyle 5^2=x^2+3^2\)

Then, fill in the remaining ratios (could be in QI or QII).

\(\displaystyle \tan u=\frac{y}{x} \: \: \: \cot u = \frac{x}{y}\)

\(\displaystyle \cos u=\frac{x}{r} \: \: \: \sec u = \frac{x}{r}\)

\(\displaystyle \sin u=\frac{y}{r} \: \: \: \csc u = \frac{r}{y}\)

Do something similar with \(\displaystyle \cos u = \frac{7}{25}\). Could be in QI or QIV.
 
May 2010
3
0
Thanks a lot man.

I have one more if you don't mind.

2sin2x-1=0