1. ## Angle measures in radians & degrees

just a couple problems i need some help with.

1. Find the measure of the angle in radians and degrees.
sin^-1 (0.6)

2. Find the six trigonometric values of theta= cos^-1 (3/7). Give exact answers. I remember doing this during the school year but it's been a long summer and i've competely lost touch with this topic unfortunately

3. Solve for x: e^-0.2x = 4

2. Originally Posted by fezz349
just a couple problems i need some help with.

1. Find the measure of the angle in radians and degrees.
sin^-1 (0.6)

2. Find the six trigonometric values of theta= cos^-1 (3/7). Give exact answers. I remember doing this during the school year but it's been a long summer and i've competely lost touch with this topic unfortunately

3. Solve for x: e^-0.2x = 4

Take the natural log of both sides.

$\displaystyle \ln(e^{-0.2x})=\ln(4)$

Also remember the rule that $\displaystyle \ln(a^b)=b\ln(a)$

3. right, so i took what u said and got 0.2xlne = ln4

i feel like this is wrong but i divide ln4 by ln of e in my calculator. it shows as ln(e^( . so i'm assuming the is being raised to the first power right? I got 1.386294361. Then divide by 0.2 on each side and my final answer was x=6.931471806. Just doesn't sound right to me for some reason.

4. $\displaystyle \ln(e)=1$

That's a very important identity. I wouldn't a decimal answer. Just keep the natural logs as is.

5. Gotcha, it's starting to come back to me now from precalc last year. Just another quick question, from the six trig functions questions, i thoguht about it for a bit and cos^-1 = (3/7) is equivalent to secant=3/7 right? Meaning cosine would be 7/3. I draw my triangle, and solve for the last side by using pythagorean theorem... i think

6. Originally Posted by fezz349
Gotcha, it's starting to come back to me now from precalc last year. Just another quick question, from the six trig functions questions, i thoguht about it for a bit and cos^-1 = (3/7) is equivalent to secant=3/7 right? Meaning cosine would be 7/3. I draw my triangle, and solve for the last side by using pythagorean theorem... i think
No, that's not true. It's a common mistake. cos^(-1) means inverse cosine, not 1 over cosine. When you take the cosine of an angle you get a ratio. When you are given a ratio you use the inverse function to find the angle.