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Sine is = to opposite side/hypotenuse,
using a triangle with sides of opposite ~ 1, adjacent ~ 1 and hypotenuse ~ root(2),
hypotenuse is always positive,
hypotenuse = root(adjacent.squared * opposite.squared)
if either is negative, squaring them brings it back to a positive
and as the opposite side is the rise from the base line ( 0 degrees through to 180 degrees) it is positive in both quadrants 1 and 2
in quadrant 1, sine= 1/root(2) which is positive
in quadrant 2, sine= 1/root(2) which is positive
in quadrant 3, sine= -1/root(2) which is negative
in quadrant 4, sine= -1/root(2) which is negative
so sine is positive in quadrants 1 and 2 and is negative in 3 and 4
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How do you solve 2 sin squared theta equals 1?
first divide each side by 2 so you get... sine^2(X)=1/2 Then make sine ^2(X)=sine(x^2) SO you get... sine(X^2)=1/2 Then take the sine^-1 of each side it will look like this X^2=sine^-1(1/2) type the right side into a calc which will give you a gross decimal but it works (0.5235987756) so now you have X^2=0.5235987756 then take the square root of each side to make it linear and you will get X=.7236012546 and that is your answer!!!! make sure to check it on your calculator...I did and it worked * * * * * Not quite correct, I fear. Try this: Let s = sin θ. Then, 2s2 = 1; s2 = ½; and s = ±½√2. Therefore, θ = 45°, 135°, 225°, or 315°; or, if you prefer, θ = ¼π, ¾π, 1¼π, or 1¾π.
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True, an example of this is 1 - 2 = -1 1 - -------2 is = to -15000 fact
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sin60° = √3/2
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| 1|2 | 3|4 |
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only in quadrants 2 and 3
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√ 1/2 = sine(45)= cosine(45) -Key
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1
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A sine wave centered at zero will have a positive peak that is the same magnitude as the negative peak. This can be offset so the negative peak magnitude does not match the positive peak magnitude. For example a 1volt peak - neutral sine wave could be DC offset by 1 volt so the positive peak is at 2 volts and the negative peak is at 0.
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What is arcsine?
The arcsine is the angle whose sine is equal to the given value. arcsine is also called sine inverse (sin-1 ) if sin 30o = 1/2 , then sin-1 1/2 = 30o
How are sine and cosine and secant related?
Sine and cosine are cofunctions, which means that their angles are complementary. Consequently, sin (90° - x) = cos x. Secant is the reciprocal of cosine so that sec x = 1/(cos x). Knowing these properties of trigonometric functions, among others, will really help you in other advance math courses.
Why value of sine lies between 1and -1?
2
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there is no quadrant 0... just 1 2 3 and 4.
How do you solve 2 sin squared theta equals 1?
first divide each side by 2 so you get... sine^2(X)=1/2 Then make sine ^2(X)=sine(x^2) SO you get... sine(X^2)=1/2 Then take the sine^-1 of each side it will look like this X^2=sine^-1(1/2) type the right side into a calc which will give you a gross decimal but it works (0.5235987756) so now you have X^2=0.5235987756 then take the square root of each side to make it linear and you will get X=.7236012546 and that is your answer!!!! make sure to check it on your calculator...I did and it worked * * * * * Not quite correct, I fear. Try this: Let s = sin θ. Then, 2s2 = 1; s2 = ½; and s = ±½√2. Therefore, θ = 45°, 135°, 225°, or 315°; or, if you prefer, θ = ¼π, ¾π, 1¼π, or 1¾π.
