Posted by Abbey on Sunday, January 8, 2012 at 10:34am.
solve for x in the following equations:
1) sin(arcsin x) = 1
2) 2arcsin x = 1
3) cos(arccos x) = 1/3
- trig - Reiny, Sunday, January 8, 2012 at 10:57am
think of the definition of inverse trig functions
arcsin x is the angle Ø so that sinØ = x
so let arcsin x = Ø
then we have sin Ø = 1
so if sinØ = 1 and sinØ = x
x = 1
(we could see that right away since something like sin(arcsin 30°) = 30° )
2 arcsin x = 1
arcsin x = 1/2
I know that sin π/6 = 1/2 or sin 30° = 1/2
so x = π/6 ( or 5π/6 , since the sine is also positive in quadrant II )
3. Just like in #1, x = 1/3
- trig - Abbey, Sunday, January 8, 2012 at 11:04am
Okay thank you for the help on one and three. In my book for number two it says the answer is sin1/2 which is approx. 0.479. I'm not sure how that answer comes about.
- correction - trig - Reiny, Sunday, January 8, 2012 at 11:12am
I solved as if it were 2sin x = 1
Don't know how I missed the "arc" since the whole question deals with it.
2 arcsinx = 1
arcsin x = 1/2
which by definition means
x = sin 1/2
so set your calculator to radians, and take sin .5
you will get .479...
Answer This Question
More Related Questions
- Calculus - Find the exact value of cot(arcsin(12/13)) and cos(arcsin(1.7/2)) I ...
- maths - Please can you help me with this question? Choose the option which is a ...
- math - Eliminate the parameter (What does that mean?) and write a rectangular ...
- math - Evaluate. 1. sin^-1(-1/2) 2. cos^-1[(-root 3)/2] 3. arctan[(root3)/3] 4. ...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- calculus - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x...
- Calc. - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln...
- Trigonometry - I need help with I just can't seem to get anywhere. this is as ...
- math - Evaluate. 1. sin^-1(-1/2) 2. cos^-1[(-root 3)/2] 3. arctan[(root3)/3] 4...
- Calculus - Book works out integral of sqtr(a^2-x^2)dx as a^2/2*arcsin(x/a)+x/2*...